Metformin Plus/Minus Fasting Mimicking Diet to Target the Metabolic Vulnerabilities of LKB1-inactive Lung Adenocarcinoma

FAME arm (chemo-immunotherapy + metformin + FMD): Inclusion criteria: 1. Age included between 18 and 75 years. 2. Histologically confirmed diagnosis of LKB1-inactive lung adenocarcinoma, as defined on the basis of absence of LKB1 expression at immunoistochemistry, and/or presence of pathogenic LKB1 mutations/deletions at next-generation sequencing analysis. 3. Absence of EGFR mutations, ALK and ROS-1 rearrangements, and absence of high expression of PD-L1 (≥ 50% in immunohistochemistry). 4. Advanced disease, defined as unresectable, locally advanced (stage IIIB) or metastatic (stage IV) lung adenocarcinoma, which is not candidate to be treated with concomitant or sequential definitive chemo-radiation. 5. Signed and dated informed consent, indicating that the patient has been informed on all the aspects of the study prior to the enrollment. 6. Patient's will able to respect the protocol recommendations about the FMD regimen, as well as about laboratory tests and other procedures. 7. Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1. 8. In case of presence of brain metastases, the patient can be candidated to be enrolled in the study, provided that neurologic symptoms are absent, the patient does not need radiotherapy or treatment with steroids at a dose ≥ 4 mg per day of dexamethasone or analogues. 9. Adequate bone marrow and organ function, defined as follows: * absolute neutrophil count ≥ 1.5 x 103/L; * platelet count ≥ 100 x 103/L; * hemoglobin ≥ 9.0 g/dL; * serum albumin-corrected calcium within normal range or with anomalies graded ≤ 1 according to Common Terminology Criteria for Adverse Events (CTCAE) version 4.03 if not clinically significant; * potassium within normal range or corrected with supplements; * glomerular filtration rate (GFR) \> 60 mL/min, estimated on a 24-hour urine exam and calculated from serum creatinine with Cockroft-Gault formula; * uric acid \< 10 mg/dL; * AST and ALT ≤ 2.5 times upper normal limits, or ≤ 5 times upper normal limits in case of liver metastases; * serum bilirubin \< 1.5 times upper normal limits, except for patients with Gilbert syndrome who will be considered amenable to be enrolled if total bilirubin is \< 3.0 times upper normal limits or direct bilirubin is \< 1.5 times upper normal limits; * serum albumin \> 3 g/dL. 10. Fasting plasma glucose concentration ≤ 200 mg/dL. 11. For women of childbearing potential, consent to maintain abstinence from sexual intercourse or to use highly effective contraceptive methods (that is, with a failure rate \< 1% per year) for the whole duration of the study and for almost 30 days after the conclusion of the FMD. Abstinence is acceptable only if in line with the patient's lifestyle. Adequate contraceptive methods include tube ligation, male sterilization, hormone implants, injectable or oral hormone contraceptives and some intra-uterine devices. Alternatively, two different contraceptive methods must be combined (e.g. two barrier methods like condom and cervical cap) in order to obtain a failure rate \<1% per year. Barrier methods must always be associated to a sperm killer. Exclusion criteria: 1. Previous systemic therapies for advanced lung cancer. 2. Evidence of disease relapse within 6 months from the conclusion of adjuvant or neoadjuvant platinum-based chemotherapy. 3. Diagnosis of other malignancies in the previous 5 years, except for adequately treated basal or squamous skin cancer or radically excised cervical cancers. Other malignancies diagnosed more than 5 years before the diagnosis of lung cancer must have been radically treated without evidence of relapse at the time of patient enrollment. 4. Body mass index (BMI) \< 20 kg/m2. 5. Anamnesis of alcohol abuse. 6. Non-intentional weight loss ≥ 5% in the previous 3 months, unless the patient has a BMI \> 25 kg/ m2 at the time of enrollment in the study, or non-intentional weight loss of ≥ 10% in the previous 3 months, unless the patients has a BMI \> 22 kg/m2 at the time of the enrollment in the study. In both cases, weight must have remained stable for at least one month. 7. Active pregnancy or breast feeding. 8. Active B or C hepatitis. 9. Serious infection in the previous 4 weeks before the start of FMD, including, but not limited to, potential hospitalizations for complications of infections, bacteriemia or serious pneumonitis. 10. Active autoimmune diseases requiring systemic treatments (e.g. systemic steroids or immune suppressants). 11. Recent diagnosis of hypothyroidism requiring systemic substitutive hormonal therapy and without stabilization of hormonal profile (fT3, fT4 and TSH within the normal range). 12. Diagnosis of type 1 or 2 diabetes mellitus requiring pharmacologic therapy (including, but not limited to, insulin, secretagogues and metformin). 13. Serious impairment of gastrointestinal function or gastrointestinal disease potentially altering nutrient digestion or absorption during re-alimentation phase (e.g. active gastric or intestinal ulcerative disease, uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome, small intestine resection). 14. Anamnesis of human immunodeficiency virus (HIV). 15. Anamnesis of clinically significant heart disease including: 1. angina pectoris, coronary bypass, symptomatic pericarditis, myocardial infarction in the previous 12 months from the beginning of experimental therapy; 2. congestive heart failure (NYHA III-IV). 16. Anamnesis of cardiac arrhythmias (e.g. ventricular tachycardia, chronic atrial fibrillation, complete bundle branch block, high grade atrio-ventricular block like bi-fascicular block, type II Mobitz and third grade atrio-ventricular block, nodal arrhythmias, supra-ventricular arrhythmias) or conduction abnormalities in the previous 12 months from the beginning of experimental therapy. 17. Reduction in left ventricular ejection fraction to \< 50% at the cardiac scan with radionuclides or at echocardiography. 18. Previous episodes of symptomatic hypotension leading to loss of consciousness. 19. Plasma fasting glucose ≤ 65 mg/dL. 20. Active therapy with systemic steroids at a dose ≥ 25 mg per day of prednisone or equivalent for any reason. 21. Medical or psychiatric comorbidities rendering the patient not candidate to the clinical trial, according to the investigator's judgement. 22. pO2 \< 60 mmHg, lactates above normal limits and pH value below normal limits at arterial hemogasanalysis. 23. Need for chronic oxygen therapy. 24. Other cardiac, liver, lung or renal comorbidities, not specified in the previous inclusion or exclusion criteria, but potentially exposing the patient to a high risk of lactic acidosis. MERCY arm (chemo-immunotherapy + metformin): Inclusion criteria: 1. Age ≥18 years. 2. Histologically confirmed diagnosis of LKB1-inactive lung adenocarcinoma, as defined on the basis of absence of LKB1 expression at immunoistochemistry, and/or presence of pathogenic LKB1 mutations/deletions at next-generation sequencing analysis. 3. Absence of EGFR mutations, ALK and ROS-1 rearrangements, and absence of high expression of PD-L1 (≥ 50% in immunohistochemistry). 4. Advanced disease, defined as unresectable, locally advanced (stage IIIB) or metastatic (stage IV) lung adenocarcinoma, which is not candidate to be treated with concomitant or sequential definitive chemo-radiation. 5. Signed and dated informed consent, indicating that the patient has been informed on all the aspects of the study prior to the enrollment. 6. Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1. 7. Adequate bone marrow and organ function, defined as follows: * absolute neutrophil count ≥ 1.5 x 103/L; * platelet count ≥ 100 x 103/L;- hemoglobin ≥ 9.0 g/dL; * serum albumin-corrected calcium within normal range or with anomalies graded ≤ 1 according to Common Terminology Criteria for Adverse Events (CTCAE) version 4.03 if not clinically significant; * potassium within normal range or corrected with supplements; * glomerular filtration rate (GFR) \> 60 mL/min, estimated on a 24-hour urine exam and calculated from serum creatinine with Cockroft-Gault formula; * uric acid \< 10 mg/dL; * AST and ALT ≤ 2.5 times upper normal limits, or ≤ 5 times upper normal limits in case of liver metastases; * serum bilirubin \< 1.5 times upper normal limits, except for patients with Gilbert syndrome who will be considered amenable to be enrolled if total bilirubin is \< 3.0 times upper normal limits or direct bilirubin is \< 1.5 times upper normal limits; * serum albumin \> 3 g/dL. 8. For women of childbearing potential, consent to maintain abstinence from sexual intercourse or to use highly effective contraceptive methods (that is, with a failure rate \< 1% per year) for the whole duration of the study and for almost 30 days after the conclusion of the metformin treatment. Abstinence is acceptable only if in line with the patient's lifestyle. Adequate contraceptive methods include tube ligation, male sterilization, hormone implants, injectable or oral hormone contraceptives and some intra-uterine devices. Alternatively, two different contraceptive methods must be combined (e.g. two barrier methods like condom and cervical cap) in order to obtain a failure rate \<1% per year. Barrier methods must always be associated to a sperm killer. Exclusion criteria: 1. Previous systemic therapies for advanced lung cancer. 2. Evidence of disease relapse within 6 months from the conclusion of adjuvant or neoadjuvant platinum-based chemotherapy. 3. Diagnosis of other malignancies in the previous 5 years, except for adequately treated basal or squamous skin cancer or radically excised cervical cancers. Other malignancies diagnosed more than 5 years before the diagnosis of lung cancer must have been radically treated without evidence of relapse. 4. Anamnesis of alcohol abuse. 5. Active pregnancy or breast feeding. 6. Active B or C hepatitis. 7. Serious infection in the previous 4 weeks before the start of metformin treatment, including, but not limited to, potential hospitalizations for complications of infections, bacteriemia or serious pneumonitis. 8. Active autoimmune diseases requiring systemic treatments (e.g. systemic steroids or immune suppressants). 9. Recent diagnosis of hypothyroidism requiring systemic substitutive hormonal therapy and without stabilization of hormonal profile (fT3, fT4 and TSH within the normal range). 10. Diagnosis of type 1 or 2 diabetes mellitus requiring pharmacologic therapy (including, but not limited to, insulin, secretagogues and metformin). 11. Serious impairment of gastrointestinal function or gastrointestinal disease potentially altering nutrient digestion or absorption during re-alimentation phase (e.g. active gastric or intestinal ulcerative disease, uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome, small intestine resection). 12. Anamnesis of human immunodeficiency virus (HIV). 13. Anamnesis of clinically significant heart disease including: 1. angina pectoris, coronary bypass, symptomatic pericarditis, myocardial infarction in the previous 12 months from the beginning of experimental therapy; 2. congestive heart failure (NYHA III-IV). 14. Anamnesis of cardiac arrhythmias (e.g. ventricular tachycardia, chronic atrial fibrillation, complete bundle branch block, high grade atrio-ventricular block like bi-fascicular block, type II Mobitz and third grade atrio-ventricular block, nodal arrhythmias, supra-ventricular arrhythmias) or conduction abnormalities in the previous 12 months from the beginning of experimental therapy. 15. Reduction in left ventricular ejection fraction to \< 50% at the cardiac scan with radionuclides or at echocardiography. 16. Medical or psychiatric comorbidities rendering the patient not candidate to the clinical trial, according to the investigator's judgement. 17. pO2 \< 60 mmHg, lactates above normal limits and pH value below normal limits at arterial hemogasanalysis. 18. Need for chronic oxygen therapy. 19. Other cardiac, liver, lung or renal comorbidities, not specified in the previous inclusion or exclusion criteria, but potentially exposing the patient to a high risk of lactic acidosis. BORN (observational arm): Inclusion criteria: 1. Age ≥18 years. 2. Histologically confirmed diagnosis of LKB1-inactive lung adenocarcinoma, as defined on the basis of absence of LKB1 expression at immunoistochemistry, and/or presence of pathogenic LKB1 mutation at next-generation sequencing analysis. 3. Absence of EGFR mutations, ALK and ROS-1 rearrangements, and absence of high expression of PD-L1 (≥ 50% in immunohistochemistry). 4. Advanced disease, defined as unresectable, locally advanced (stage IIIB) or metastatic (stage IV) lung adenocarcinoma, which is not candidate to be treated with concomitant or sequential definitive chemo-radiation. 5. Signed and dated informed consent, indicating that the patient has been informed on all the aspects of the study prior to the enrollment. 6. At least one exclusion criteria of FAME and MERCY arm. Exclusion criteria: None Patients who are eligible for the FAME arm will be preferentially proposed to be enrolled in the FAME. If they refuse, then they will be proposed to be enrolled in the MERCY arm. If they also refuse to be enrolled in the MERCY arm, they will be proposed to be enrolled in the BORN arm. Patients who are eligible for the MERCY arm will be preferentially proposed to be enrolled in the MERCY arm; if they refuse, the will be proposed to be enrolled in the BORN arm. Finally, patients who are ineligible for both the FAME and MERCY arms will be proposed to be enrolled in the BORN arm.