Alisertib in Combination With Osimertinib in Metastatic EGFR-mutant Lung Cancer

Inclusion Criteria: 1. Patients must have histologically confirmed stage IV non-small cell lung cancer. 2. Male or female patients \>=18 years of age 3. Eastern Cooperative Oncology Group (ECOG) performance status of 0-1. 4. Documented activating EGFR mutation (Exon 19 deletion, Exon 19 insertion, E709K, G719X, S768I, V769L, T790M, L833F, L833V, V834L, H835L, L858R, A859S, K860I, L861Q, A871E, V843I, or H870R) on tumor sample or cell-free DNA sample performed in Clinical Laboratory Improvement Amendments (CLIA)-approved laboratory. 5. Measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 criteria. 6. Clinical laboratory values as specified below within 7 days before the first dose of study drug (if applicable): 1. Absolute neutrophil count (ANC) \> 1500/mm\^3 2. Absolute lymphocyte count \> 500 mm\^3 3. Platelets \> 100,000/mm\^3 4. Hemoglobin (Hgb) \> 9 g/dL. Values must be obtained without need for red blood cell transfusion support within 14 days. However, erythrocyte growth factor is allowed as per published American Society of Clinical Oncology (ASCO) guidelines. 5. Total bilirubin ≤ 1.5 x upper limit of normal (ULN). Patients with Gilbert's syndrome may be allowed on study if total bilirubin is \<= 3 x upper limit of normal (ULN) if direct bilirubin is \<= 1.5 x upper limit of normal (ULN). 6. Serum glutamic-oxaloacetic transaminase (SGOT) / aspartate aminotransferase (AST) and serum glutamic-pyruvic transaminase (SGPT) / alanine aminotransferase (ALT) \< 2.5 x ULN. AST and/or ALT may be up to 5 x ULN if with known liver metastases. 7. Renal function as defined by calculated creatinine clearance \>=30 ml/min (Cockcroft-Gault Formula). 7. Willing to provide blood and tissue for correlative research purposes. 8. Willing to undergo pre-treatment research biopsy, OR donate archived tissue from a biopsy performed within 60 days of the first dose of study drug is available. 9. Female patients who: 1. Are postmenopausal (see Appendix 6) for at least 1 year before the screening visit, OR 2. Are surgically sterile, OR 3. If they are of childbearing potential, agree to practice 1 highly effective method of contraception and 1 additional effective (barrier) method at the same time (see Appendix 6), from the time of signing the informed consent through 180 days after the last dose of study drug, OR 4. Agree to practice true abstinence, when this is in line with the preferred and usual lifestyle of the subject. (Periodic abstinence \[e.g., calendar, ovulation, symptothermal, post-ovulation methods\], withdrawal, spermicides only, and lactational amenorrhea are not acceptable methods of contraception. Female and male condoms should not be used together.) 10. Male patients, even if surgically sterilized (i.e., status post-vasectomy), who: 1. Agree to practice effective barrier contraception during the entire study treatment period and through 120 after the last dose of study drug, OR 2. Agree to practice true abstinence, when this is in line with the preferred and usual lifestyle of the subject. (Periodic abstinence \[e.g., calendar, ovulation, symptothermal, post-ovulation methods\], withdrawal, spermicides only, and lactational amenorrhea are not acceptable methods of contraception. Female and male condoms should not be used together.) 11. Voluntary written consent must be given before performance of any study-related procedure not part of standard of care, with the understanding that consent may be withdrawn by the patient at any time without prejudice to future medical care. 12. Currently receiving and tolerating osimertinib 80 mg PO daily with no current grade 2 or greater AE attributable to osimertinib. 13. Evidence of disease progression on imaging (computerized tomography (CT) scan, magnetic resonance imaging (MRI), or Positron Emission Tomography (PET) CT within the last 30 days. 14. Resolution of all acute toxic effects of prior chemotherapy, immunotherapy, radiotherapy or surgical procedures to less than or equal to grade 2 per the National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) Version 5.0. Inclusion Criteria (Cohort A): Must meet inclusion criteria below in addition to 1-14 above: 15. Patients must have received no more than one additional line of systemic therapy to treat lung cancer other than osimertinib (re-treatment with osimertinib after other systemic lung cancer therapy will not count as a line of therapy). A line of therapy equals at least one month of treatment with discontinuation of therapy due to disease progression or intolerability. Patients who have received adjuvant or neoadjuvant osimertinib, chemotherapy, or immunotherapy for surgically resectable NSCLC, or chemotherapy + radiation +/- immunotherapy for locally advanced NSCLC, will not be considered a line of therapy if it is equal to or greater than 12 months since completing their treatment. 16. Patients must be currently receiving osimertinib 80 mg for the treatment of metastatic disease or have evidence of metastatic disease recurrence while receiving adjuvant osimertinib therapy. Inclusion Criteria (Cohort B): Must meet inclusion criteria below in addition to 1-7, 9-12, and 14. Inclusion criteria 8 and 13 are not required. The following inclusion criteria must also be met: 17. Currently receiving osimertinib 80 mg as 1st line therapy for metastatic NSCLC. Patients who have received adjuvant or neoadjuvant, chemotherapy, or immunotherapy for surgically resectable NSCLC, or chemotherapy + radiation +/- immunotherapy for locally advanced NSCLC, will be allowed if it is equal to or greater than 12 months since completing their treatment. 18. Meet RECIST 1.1 criteria for PR or SD to osimertinib, including a confirmation scan. 19. Have received osimertinib 80 mg for a minimum of 90 days, but no more than 180 days. Inclusion Criteria (Cohort C): Must meet inclusion criteria 1-7 and 9-16 above. The following inclusion criterion must also be met: 20. Willing to undergo pre-treatment research biopsy, if deemed safe by the investigator, or willing to donate archived tissue from a biopsy performed within 60 days prior to the first dose of study drug. Note: Pre-treatment tissue is mandatory for Cohort C and will be used for a CLIA-approved TP53 mutation test during screening. To be eligible for Cohort C, patients must not have a known TP53 missense mutation, nonsense mutation, frameshift mutation, in frame deletion, or whole gene deletion (see also exclusion criterion #22). Exclusion Criteria 1. Radiation therapy to more than 25% of the bone marrow. Whole pelvic radiation is considered to be over 25%. 2. Prior allogeneic bone marrow or organ transplantation 3. Known Gastrointestinal (GI) disease or GI procedures that could interfere with the oral absorption or tolerance of alisertib. Examples include, but are not limited to partial gastrectomy, history of small intestine surgery, and celiac disease 4. Inability to swallow oral medication or inability or unwillingness to comply with the administration requirements related to alisertib. 5. Known history of uncontrolled sleep apnea syndrome and other conditions that could result in excessive daytime sleepiness, such as severe chronic obstructive pulmonary disease; requirement for supplemental oxygen. 6. Requirement for constant administration of proton pump inhibitor, Histamine 2 (H2) antagonist, or pancreatic enzymes throughout the study. The intermittent use of H2-antagonists and antacids (including carafate) is only allowed within these guidelines: 1. H2 antagonists until Day -1 and after the dosing of alisertib is done 2. Antacid formulations until 2 hours before dosing and after 2 hours following dosing. 3. Proton Pump Inhibitor (PPI) is allowed until Day -5 of first alisertib dose. PPIs are prohibited throughout the study. 7. Myocardial infarction within 6 months prior to enrollment or has New York Heart Association (NYHA) Class III or IV heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia or active conduction system abnormalities. Prior to study entry, any electrocardiogram (ECG) abnormality at Screening has to be documented by the investigator as not medically relevant. 8. QT interval corrected (QTc) using Fridericia's method (QTCF) \> 470 milliseconds (msec). The following formula can be used to calculate QTcF for subjects with a wide QRS complex caused by the bundle branch block, QTcF = measured QTcF - (QRS - 100msec). 9. Female subject who is pregnant or breast-feeding. Confirmation that the subject is not pregnant must be established by a negative serum beta-human chorionic gonadotropin (Beta-hCG) pregnancy test result obtained during screening. Pregnancy testing is not required for post-menopausal or surgically sterilized women. 10. Female patient who intend to donate eggs (ova) during the course of this study or 4 months after receiving their last dose of study drug(s). 11. Male patients who intend to donate sperm during the course of this study or 4 months after receiving their last dose of study drug(s). 12. Other severe acute or chronic medical or psychiatric condition, including uncontrolled diabetes, malabsorption, resection of the pancreas or upper small bowel, requirement for pancreatic enzymes, any condition that would modify small bowel absorption of oral medications, or laboratory abnormality that may increase the risk associated with study participation or investigational product administration or may interfere with the interpretation of study results and, in the judgment of the investigator, would make the patient inappropriate for enrollment in this study. 13. Diagnosed or treated for another malignancy within 3 years of enrollment, with the exception of complete resection of basal cell carcinoma or squamous cell carcinoma of the skin, an in situ malignancy, or low-risk prostate cancer or breast cancer, or thyroid cancer after curative therapy 14. Patients who are currently receiving treatment with contraindicated QTcF prolonging medications or potent CYP3A4 inducers/inhibitors if that treatment cannot be either discontinued or switched to a different medication prior to first day of study treatment. 15. Patients with central nervous system (CNS) metastases who are neurologically unstable (as defined by need for steroids in last 14 days). 16. Known leptomeningeal carcinomatosis. Exclusion Criteria (Cohort A): Must meet exclusion criteria 1-16 above. The following exclusion criteria must also be met: 17. Known small cell lung cancer transformation on osimertinib resistance biopsy. 18. Known EGFR C797S osimertinib resistance mutation, hepatocyte growth factor receptor (MET) amplification, oncogenic fusion involving neurotrophic tyrosine receptor kinase (NTRK), RET, ALK, ROS-1, or BRAF, BRAF V600E, or oncogenic KRAS mutation determined by Clinical Laboratory Improvement Amendments (CLIA)-approved test on osimertinib resistance biopsy or cell-free deoxyribonucleic acid (DNA) test performed at osimertinib resistance. Exclusion Criteria (Cohort B): Must meet exclusion criteria 1-16 above. The following exclusion criteria must also be met: 19. Evidence of complete response (CR) or progressive disease (PD) to osimertinib by RECIST 1.1 criteria on imaging within 30 days prior to starting alisertib. 20. Prior treatment with adjuvant osimertinib. 21. Prior treatment with an EGFR TKI other than osimertinib. Exclusion Criteria (Cohort C): Must not meet exclusion criteria 1-18 above. The following exclusion criterion must also not be met: 22. Known TP53 missense mutation, nonsense mutation, frameshift mutation, in frame deletion, or whole gene deletion determined by CLIA-approved test on any prior patient lung cancer biopsy.