S1800D: Phase II/III Study of N-803 (ALT-803) Plus Pembrolizumab Vs. Standard of Care in Participants with Stage IV or Recurrent Non-Small Cell Lung Cancer Previously Treated with Anti-PD-1 orAnti-PD-L1 Therapy (Lung-MAP Non-Match Sub-Study)

Inclusion Criteria:
*  Participants must have been assigned to S1800D by the Southwest Oncology Group (SWOG) Statistics and Data Management Center (SDMC). Assignment to S1800D is determined by the LUNGMAP or S1400 protocol
*  Participants must have measurable or non-measurable disease documented by computed tomography (CT) or magnetic resonance imaging (MRI). Measurable disease must be assessed within 28 days prior to randomization. Non-measurable disease must be assessed within 42 days prior to randomization. The CT from a combined positron emission tomography (PET)/CT may be used only if it is of diagnostic quality. All known sites of disease must be assessed and documented on the Baseline Tumor Assessment Form (RECIST 1.1)
*  Participants must have a CT or MRI scan of the brain to evaluate for central nervous system (CNS) disease within 42 days prior to sub-study randomization
*  Participants with spinal cord compression or brain metastases must have received local treatment to these metastases and remained clinically controlled and asymptomatic for at least 7 days following stereotactic radiation and/or 14 days following whole brain radiation, and prior to sub-study randomization
*  Participants with spinal cord compression or brain metastases must not have residual neurological dysfunction, unless no further recovery is expected, and the participant has been stable on weaning doses of corticosteroids (=\< 10 mg daily prednisone or equivalent) prior to sub-study randomization
*  Participants must have progressed (in the opinion of the treating investigator) following the most recent line of therapy for non-small cell lung cancer (NSCLC)
*  Participants with a known sensitizing mutation for which an FDA-approved targeted therapy for NSCLC exists (e.g. EGFR, ALK gene fusions, ROS1, BRAF, RET, NTRK, and MET sensitizing mutations), must have previously received at least one of the approved therapy(s)
*  Participants must have received exactly one line of anti-PD-1 or anti-PD-L1 therapy for advanced disease (stage IV or recurrent, or stage III in certain circumstances outlined below) given alone or in combination with platinum-based chemotherapy. Participants must have experienced disease progression during or after this regimen
*  Continuing the same agent(s) after progression counts as a single line of therapy. However, a change or addition in agent(s) after progression (e.g. the addition of chemotherapy to anti-PD-1 monotherapy after progression) counts as a subsequent line of therapy and would exclude the participant
*  For participants who received consolidation anti-PD-1 or anti-PD-L1 therapy following concurrent chemoradiation for Stage III disease as their only line of anti-PD-1 or anti-PD-L1 therapy:
*  If they experienced disease progression less than (\<) 365 days from the first date of anti-PD-1 or anti-PD-L1 therapy, this counts as the single line of anti-PD-1 or anti-PD-L1 therapy for advanced disease
*  If they experienced disease progression more than or equal to (\>=) 365 days from the first date of anti-PD-1 or anti-PD-L1 therapy, this is not considered a line of anti-PD-1 or anti-PD-L1 therapy for advanced disease
*  Participants must have recovered (=\< grade 1) from any side effects of prior therapy, except for alopecia
*  Participants must be able to safely receive at least one of the investigator's choice of standard of care regimens, per the current FDA-approved package insert
*  Note: Pemetrexed is not FDA-approved for squamous cell NSCLC and must not be used to treat participants with squamous cell NSCLC
*  Absolute neutrophil count (ANC) \>= 1.5 x 10\^3/uL (obtained within 28 days prior to sub-study randomization)
*  Platelet count \>= 100 x 10\^3/uL(obtained within 28 days prior to sub-study randomization)
*  Hemoglobin \>= 9 g/dL (obtained within 28 days prior to sub-study randomization)
*  Serum bilirubin =\< institutional upper limit of normal (IULN) (within 28 days prior to sub-study randomization). For participants with liver metastases, bilirubin must be =\< 5 x IULN
*  Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 2 x IULN (within 28 days prior to sub-study randomization). For participants with liver metastases, ALT and AST must be =\< 5 x IULN
*  Serum creatinine =\< the IULN or calculated creatinine clearance \>= 50 mL/min using Cockcroft-Gault formula. This specimen must have been drawn and processed within 28 days prior to sub-study randomization
*  Participants' most recent Zubrod performance status must be 0-1 and be documented within 28 days prior to sub-study randomization
*  Participants must have history and physical exam must be obtained within 28 days prior to sub-study randomization
*  Participants with known human immunodeficiency virus (HIV) infection must be receiving anti-retroviral therapy and have an undetectable viral load at their most recent viral load test within 6 months prior to sub-study randomization
*  Participants must also be offered participation in banking and in the correlative studies for collection and future use of specimens
*  Note: As a part of the OPEN registration process the treating institution's identity is provided in order to ensure that the current (within 365 days) date of institutional review board approval for this study has been entered in the system
*  Participants must be informed of the investigational nature of this study and must sign and give written informed consent in accordance with institutional and federal guidelines

Exclusion Criteria:
*  Participants must not have leptomeningeal disease that requires CNS-specific treatment prior to registration and must not be planning to receive the CNS-specific treatment through the first cycle of the protocol therapy
*  Participants must not have experienced the following:
*  Any grade 3 or worse immune-related adverse event (irAE). Exception: asymptomatic nonbullous/nonexfoliative rash
*  Any unresolved grade 2 irAE
*  Any toxicity that led to permanent discontinuation of prior anti-PD-1/PD-L1 immunotherapy
*  Exception to the above: Toxicities of any grade that requires replacement therapy and has stabilized on therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency) are allowed
*  Participants must not have any history of organ transplant that requires use of immunosuppressives
*  Participants must not have history of (non-infectious) pneumonitis that required steroids or current pneumonitis/interstitial lung disease
*  Participants must not have any known allergy or reaction to any component of the investigational formulations. If there is a known allergy or reaction to standard of care formulations, participants must be able to safely receive at least one of the standard of care options
*  Participants must not have any grade III/IV cardiac disease as defined by the New York Heart Association Criteria (i.e., participants with cardiac disease resulting in marked limitation of physical activity or resulting in inability to carry on any physical activity without discomfort), unstable angina pectoris, and myocardial infarction within 6 months prior to sub-study randomization, or serious uncontrolled cardiac arrhythmia
*  Participants must not have experienced any arterial thromboembolic events, including but not limited to myocardial infarction, transient ischemic attack, cerebrovascular accident, or unstable angina, within 6 months prior to sub-study randomization
*  Participants must not have an active or uncontrolled infection in the opinion of the treating investigator
*  Participants must not have a prior or concurrent malignancy whose natural history or treatment has the potential to interfere with the safety or efficacy assessment of the investigational regimen
*  Participants must not have any of following:
*  Cirrhosis at a level of Child-Pugh B (or worse)
*  Cirrhosis (any degree) and a history of hepatic encephalopathy
*  Or clinically meaningful ascites resulting from cirrhosis. Clinically meaningful ascites is defined as ascites from cirrhosis requiring diuretics or paracentesis
*  Participants must not have received anti-CTLA4 therapy (e.g. ipilimumab, tremelimumab), or other immune-modulatory therapy (e.g. anti-TIM-3, anti-LAG-3, anti-GITR, IL-2, IL-15)
*  Participants must not have received any prior systemic therapy (systemic chemotherapy, immunotherapy or investigational drug) within 21 days prior to sub-study randomization
*  Participants must not have received any radiation therapy within 14 days prior to sub-study randomization
*  Participants must not have received nitrosoureas or mitomycin-c within 42 days prior to sub-study randomization
*  Participants must not have received systemic treatment with corticosteroids (\> 10 mg daily prednisone or equivalent) or other immunosuppressive medications within 7 days prior to sub-study randomization. Inhaled or topical steroids, and adrenal replacement doses =\< 10 mg daily prednisone or equivalent are permitted in the absence of active autoimmune disease
*  Participants must not have received a live attenuated vaccination within 28 days prior to sub-study randomization. All COVID-19 vaccines that have received Food and Drug Administration (FDA) approval or FDA emergency use authorization are acceptable
*  Participants must not be planning to receive any concurrent chemotherapy, immunotherapy, biologic or hormonal therapy for cancer treatment while receiving treatment on this study
*  Participants must not have had a major surgery within 14 days prior to sub-study randomization. Participant must have fully recovered from the effects of prior surgery in the opinion of the treating investigator
*  Participants must not have an active autoimmune disease that has required systemic treatment within two years prior to sub-study randomization (i.e., with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency) is not considered a form of systemic treatment and is allowed
*  Participants must not have any history of primary immunodeficiency
*  Participants must not be pregnant or nursing. Women/men of reproductive potential must have agreed to use an effective contraceptive method during the study and 4 months after completion of study treatment. A woman is considered to be of "reproductive potential" if she has had menses at any time in the preceding 12 consecutive months. In addition to routine contraceptive methods, "effective contraception" also includes heterosexual celibacy and surgery intended to prevent pregnancy (or with a side-effect of pregnancy prevention) defined as a hysterectomy, bilateral oophorectomy or bilateral tubal ligation. However, if at any point a previously celibate participant chooses to become heterosexually active during the time period for use of contraceptive measures outlined in the protocol, he/she is responsible for beginning contraceptive measures during the study and 4 months after study completion