Immunotherapy Biomarkers to Predict First-line PD(L)1-based Immunotherapy Response and Selection of Second-line Treatment in Stage IIIB-IV Non-small Cell Lung Cancer, IMMUNO-BIOMAP Trial

Inclusion Criteria: * Documented informed consent of the participant and/or legally authorized representative. (Adult patients lacking capacity to consent may participate if they have a caretaker that could ensure compliance.) * Participants must have either A) HopeSeq or Tempus molecular testing results reported within 3 months prior to enrollment or currently in process OR B) archival or new biopsy tissue available (to be sent to Tempus). Acceptable sample types include: two formalin-fixed paraffin-embedded (FFPE) tissue core biopsies, or two 25um sections of 5-10mm\^2 tissue, or 15-20 unstained slides at 10um thickness (a minimum of 10 unstained slides must be provided) * Agreement to blood collection for ctDNA research * Age: ≥ 18 years * Eastern Cooperative Oncology Group (ECOG) ≤ 2 * Histologically confirmed stage IIIB or IV NSCLC * Absence of sensitizing EGFR mutation or ALK/ROS1 alteration * Scheduled to begin treatment with a Food and Drug Administration (FDA) approved PD1/PDL1 antibody with or without chemotherapy. Participants who have already started treatment with anti-PD1/PDL1 in this setting may enroll if they have only received up to 4 cycles of treatment so far. Patients who have received PD1/PDL1 antibody for early-stage NSCLC are allowed to enroll if they completed the therapy at least 6 months before starting trial therapy * Measurable disease by RECIST version (v) 1.1 * Absolute neutrophil count (ANC) ≥ 1,500/mm\^3 * NOTE: Growth factor is not permitted within 14 days of ANC assessment * Platelets ≥ 100,000/mm\^3 * NOTE: Platelet transfusions are not permitted within 14 days of platelet assessment * Hemoglobin ≥ 9g/dL * NOTE: Red blood cell transfusions are not permitted within 14 days of hemoglobin assessment * Total bilirubin ≤ 1.5 x upper limit of normal (ULN) * Aspartate aminotransferase (AST) ≤ 3.0 x ULN (5 x ULN allowed if liver metastases) * Alanine aminotransferase (ALT) ≤ 3.0 x ULN (5 x ULN allowed if liver metastases) * Creatinine clearance of ≥ 50 mL/min per the Cockcroft-Gault formula * If seropositive for HIV, hepatitis C virus (HCV), or hepatitis B virus (HBV), nucleic acid quantitation must be performed. Viral load must be undetectable * HIV-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial * Women of childbearing potential (WOCBP): negative urine or serum pregnancy test * If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Agreement by females and males of childbearing potential to use an effective method of birth control or abstain from heterosexual activity for the course of the study through at least 3 months after the last dose of protocol therapy * Childbearing potential defined as not being surgically sterilized (men and women) or have not been free from menses for \> 1 year (women only) * PART II: Documented informed consent (for Part II) of the participant and/or legally authorized representative. * Assent, when appropriate, will be obtained per institutional guidelines * PART II: ECOG ≤ 2 * PART II: Fully recovered from the acute toxic effects (except alopecia) to ≤ grade 1 to prior anti-cancer therapy * PART II: ANC ≥ 1,500/mm\^3 * NOTE: Growth factor is not permitted within 14 days of ANC assessment * PART II: Platelets ≥ 100,000/mm\^3 * NOTE: Platelet transfusions are not permitted within 14 days of platelet assessment * PART II: Hemoglobin ≥ 9g/dL * NOTE: Red blood cell transfusions are not permitted within 14 days of hemoglobin assessment * PART II: Total bilirubin ≤ 1.5 x ULN * PART II: AST ≤ 3.0 x ULN (5 x ULN allowed if liver metastases) * PART II: ALT ≤ 3.0 x ULN (5 x ULN allowed if liver metastases) * PART II: Creatinine clearance of ≥ 50 mL/min per the Cockcroft-Gault formula Exclusion Criteria: * Surgical intervention within 4 weeks prior to study treatment, except for minor procedures such as port placement * Patients with a condition requiring systemic treatment with corticosteroids (\> 10 mg daily prednisone equivalent) within 7 days or another immunosuppressive medication within 30 days of the first dose of study treatment. Inhaled or topical steroids, and adrenal replacement steroid doses ≤ 10 mg daily prednisone equivalent, are permitted in the absence of active autoimmune disease * Radiation therapy within 7 days prior to day 1 of protocol therapy * Clinically significant (i.e., active) cardiovascular disease: cerebral vascular accident/stroke or myocardial infarction within 6 months of enrollment, unstable angina, congestive heart failure (New York Heart Association \[NYHA class\] ≥ III), or serious uncontrolled cardiac arrhythmia requiring medication * Active autoimmune disease or history of autoimmune disease that required systemic treatment within 2 years before starting treatment, i.e., with use of disease-modifying agents or immunosuppressive drugs * Symptomatic central nervous system (CNS) metastases or leptomeningeal carcinomatosis, except for individuals who have 1) previously-treated CNS metastases, are asymptomatic, and have had no requirement for steroid medication for 1 week prior to the first dose of study drug and have completed radiation 2 weeks prior to the first dose of study drug OR 2) untreated brain metastases that are asymptomatic and stable * Prior history of interstitial lung disease (ILD) or non-infectious pneumonitis requiring high-dose glucocorticoids * Active infection requiring antibiotics * Other active malignancy. Patients with concurrent malignancy other than non-melanoma skin cancer are not eligible for this trial due to potential confounding of the ctDNA results * Females only: Pregnant or breastfeeding * PART II: Surgical intervention within 4 weeks prior to study treatment, except for minor procedures such as port placement * PART II: Radiation therapy within 7 days prior to day 1 of protocol therapy * PART II ARM A ONLY: Pa