This phase III trial compares the effect of the combination of ramucirumab and pembrolizumab versus standard of care chemotherapy for the treatment of non-small cell lung cancer that is stage IV or that has come back after a period of improvement (recurrent). Ramucirumab is a monoclonal antibody that may prevent the growth of new blood vessels that tumors need to grow. Immunotherapy with monoclonal antibodies, such as pembrolizumab, may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. Chemotherapy drugs work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. This trial may help doctors find out if giving ramucirumab with pembrolizumab is more effective at treating patients with stage IV or recurrent non-small cell lung cancer than standard chemotherapy.

PRIMARY OBJECTIVE:

I. To compare overall survival (OS) in participants previously treated with platinum-based chemotherapy and immunotherapy for stage IV or recurrent non-small cell lung cancer (NSCLC) randomized to pembrolizumab and ramucirumab versus standard of care.

SECONDARY OBJECTIVE:

I. To summarize reports of serious and unexpected high-grade (>= grade 3) treatment-related adverse events determined by the treating physician within each treatment arm.

OUTLINE: Patients are randomized to 1 of 2 arms.

ARM A: Patients receive chemotherapy per standard of care on study.

ARM B: Patients receive ramucirumab intravenously (IV) and pembrolizumab IV on study.

Inclusion Criteria:

• Participants must have histologically or cytologically confirmed non-small cell lung cancer (NSCLC) which is stage IV or recurrent
• Participants must have received at least one line of anti-PD-1 or anti-PD-L1 therapy for any stage of NSCLC. Anti-PD-1 or anti-PD-L1 may have been given alone or in combination with other therapy
• Participants must have experienced disease progression (in the opinion of the treating physician) more than (>) 84 days following initiation (cycle 1 day 1) of their most recent anti-PD-1 or PD-L1 therapy
• Participants who received anti-PD-1 or anti-PD-L1 therapy for stage IV or recurrent disease, must have had a best response on anti-PD-1 or anti-PD-L1 therapy of stable, partial response or complete response (in the opinion of the treating physician)
• Participants who received neoadjuvant, adjuvant, and/or consolidation anti-PD-1 or anti-PD-L1 therapy as their only line of anti-PD-1 or anti-PD-L1 therapy must have experienced disease progression within (=<) 365 days from initiation (cycle 1 day 1) of anti-PD-1 or PD-L1 therapy
• Participants must have received platinum-based chemotherapy and experienced disease progression (in the opinion of the treating physician) during or after this regimen
• Participants with a known sensitizing mutation for which an Food and Drug Administration (FDA)-approved targeted therapy for NSCLC exists (e.g., EGFR, ALK, ROS1, BRAF, RET, NTRK, KRAS, HER2 and MET sensitizing mutations), must have previously received at least one of the approved therapy(s). Prior targeted therapy for participants with targetable alterations is allowed if all other eligibility criteria are also met
• Participants must be >= 18 years old
• Participants must be able to safely receive the investigational drug combination and the investigator's choice of standard of care regimens per the current FDA approved package insert(s), treating investigator's discretion, and institutional guidelines
• Participants must have Zubrod performance status of 0-2

Exclusion Criteria:

• Participants must not have received more than one line of anti-PD-1 or anti-PD-L1 for stage IV or recurrent disease
• Participants must not be receiving or planning to receive another investigational therapy during study participation