Personalized Therapeutic Anti-tumor Vaccine With Pembrolizumab and Standard of Care Chemotherapy in Squamous Non-Small Cell Lung Cancer and Extensive Stage Small Cell Lung Cancer

Inclusion Criteria: * Cohort A: Histologically confirmed stage IV squamous NSCLC * Cohort B: Histologically confirmed extensive stage SCLC * Sufficient tumor tissue must be available for histologic assessment of PD-L1 expression and for sequence and immunological analysis. * Measurable disease by RECIST 1.1. Lesions situated in a previously irradiated area are considered measurable if progression has been demonstrated in such lesions. * At least 18 years of age on the day of signing informed consent. * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * Normal bone marrow and organ function as defined in the table below within 10 days of study entry: * Absolute neutrophil count (ANC): ≥1500/µL * Platelets: ≥100 000/µL * Hemoglobin: ≥9.0 g/dL or ≥5.6 mmol/L (Criteria must be met without erythropoietin dependency and without packed red blood cell (pRBC) transfusion within last 2 weeks) * Creatinine: ≤1.5 × upper limit of normal (ULN) OR * Measured or calculated2 creatinine clearance (GFR can also be used in place of creatinine or CrCl): ≥30 mL/min for patient with creatinine levels / \>1.5 × institutional ULN * Total bilirubin: ≤1.5 ×ULN OR direct bilirubin ≤ULN for patients with total bilirubin levels \>1.5 × ULN * AST (SGOT) and ALT (SGPT): ≤2.5 × ULN (≤5 × ULN for patients with liver metastases) * International normalized ratio (INR) OR prothrombin time (PT) activated partial thromboplastin time (aPTT): ≤1.5 × ULN unless patient is receiving anticoagulant therapy as long as PT or aPTT is within therapeutic range of intended use of anticoagulants * Male Patients: A male patient must agree to use a contraception as detailed in this protocol during the treatment period and for at least 120 days, corresponding to time needed to eliminate any study treatment(s) after the last dose of study treatment and refrain from donating sperm during this period. * Female Patients: A female patient is eligible to participate if she is not pregnant, not breastfeeding, and at least one of the following conditions applies: A woman of childbearing potential who agrees to follow the contraceptive guidance during the treatment period and for at least 120 days (corresponding to time needed to eliminate any study treatment(s). Should a woman become pregnant or suspect she is pregnant while participating in this study, she must inform her treating physician immediately. * Ability to understand and willingness to sign an IRB approved written informed consent document (or that of legally authorized representative, if applicable). Exclusion Criteria: * Cohort A: Received any prior systemic therapy for cancer treatment. * Cohort B: May not have received more than one cycle of platinum doublet given with or without an anti-PD-1 or anti-PD-L1 immunotherapeutic. * Prior chemotherapy, targeted small molecule therapy, or radiation therapy within 14 days prior to day 1 or who has not recovered (ie, ≤ Grade 1 or at baseline from adverse events due to previous therapies). Patients with ≤Grade 2 neuropathy may be eligible. Note: If patient received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting study treatment. * Received prior radiotherapy within 2 weeks of start of study treatment. Patients must have recovered from all radiation-related toxicities, not require corticosteroids, and not have had radiation pneumonitis. A 1-week washout is permitted for palliative radiation (≤2 weeks of radiotherapy) to non-CNS disease. * Patients may not receive or have received any radiation therapy at the biopsy sites. * Is currently participating in or has participated in a study of an investigational agent or has used an investigational device within 4 weeks prior to the first dose of study treatment. Note: Patients who have entered the follow-up phase of an investigational study may participate as long as it has been 4 weeks after the last dose of the previous investigational agent. * Has had an allogeneic tissue/solid organ transplant. * Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy \> 10 mg prednisone daily or any other form of immunosuppressive therapy within 7 days prior to Day 1. * Prior treatment with an anti-PD-1, anti-PD-L1, or anti-PD-L2 agent. * Prior treatment with a cancer vaccine. * Prior treatment with an agent directed to another stimulatory or co-inhibitory T-cell receptor (eg, CTLA-4, OX-40, CD137). * Received a live vaccine within 30 days prior to Day 1. Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster (chicken pox), yellow fever, rabies, Bacillus Calmette-Guérin (BCG), and typhoid vaccine. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (eg, FluMist®) are live attenuated vaccines and are not allowed. * Known active CNS metastases and/or carcinomatous meningitis. Subjects with previously treated brain metastases may participate provided they are stable (without evidence of progression by imaging for at least four weeks prior to Day 1 and any neurologic symptoms have returned to baseline), have no evidence of new or enlarging brain metastases, and are not using steroids for at least 7 days prior to trial treatment. * Known additional malignancy that is progressing or has required active treatment within the past 3 years. Note: Patients with basal cell carcinoma of the skin, squamous cell carcinoma of the skin, or carcinoma in situ (eg, breast carcinoma, cervical cancer in situ) that have undergone potentially curative therapy are not excluded. -Currently receiving any other investigational agents or has participated in a study of an investigational agent or using an investigational device within 4 weeks prior to Day 1. Note: Patients who have entered the follow-up phase of an investigational study may participate as long as it has been 4 weeks after the last dose of the previous investigational agent. * A history of allergic reactions attributed to compounds of similar chemical or biologic composition to pembrolizumab or other agents used in the study. * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection requiring systemic therapy, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, underlying pulmonary disease, or psychiatric illness/social situations that would limit compliance with study requirements. * Active autoimmune disease requiring systemic treatment within the past 2 years (i.e. with use of disease modifying agents, corticosteroids (prednisone dose of 10 mg or less per day is allowed), or immunosuppressive drugs). Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment. * Known history of, or any evidence of active, non-infectious pneumonitis. * A woman of childbearing potential who has a positive urine pregnancy test within 72 hours prior to treatment allocation. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. Note: In the event that 72 hours have elapsed between the screening pregnancy test and the first dose of study treatment, another pregnancy test (urine or serum) must be performed and must be negative in order for subject to start receiving study medication. * Pregnant or breastfeeding or expecting to conceive or father children within the projected duration of the study, starting with the screening visit through 120 days after the last dose of study treatment. * Has a known history of hepatitis B (defined as hepatitis B surface antigen \[HBsAg\] reactive) or known active hepatitis C virus (defined as HCV RNA \[qualitative\] is detected) infection. Note: No testing for hepatitis B and hepatitis C is required unless mandated by local health authority. * Known history of active tuberculosis (TB). * Known history of human immunodeficiency virus (HIV) (HIV 1/2 antibodies). * Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study, interfere with the patient's participation for the full duration of the study, or is not in the best interest of the patient to participate, in the opinion of the treating investigator. * Has a known psychiatric or substance abuse disorder that would interfere with the patient's ability to cooperate with the requirements of the study.