Ramucirumab Plus Pembrolizumab vs Usual Care for Treatment of Stage IV or Recurrent Non-Small Cell Lung Cancer Following Immunotherapy, Pragmatica-Lung 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