A PET Imaging Agent (64Cu-DOTA-Pembrolizumab) for Determining Treatment Response Among Patients With Stage IV Non-small Cell Lung Cancer Receiving Pembrolizumab

Inclusion Criteria: * Documented informed consent of the participant and/or legally authorized representative * Assent, when appropriate, will be obtained per institutional guidelines * Age: ≥ 18 years * Eastern Cooperative Oncology Group (ECOG) ≤ 2 * Histologically confirmed stage IV non-small cell lung cancer * Patients on single-agent pembrolizumab, who have been referred for SBRT for or oligo-progressive disease. A maximum of 6 sites will be allowed to receive SBRT on protocol * Patients must have sites that are amenable to SBRT that are located in lymph nodes, bone/spine, or lung * Brain metastases or cases with intra-cranial progression are allowed, but an additional extra-cranial site planned for SBRT is required * Absolute neutrophil count (ANC) ≥ 1,000/mm\^3 * Platelets ≥ 50,000/mm\^3 * NOTE: Platelet transfusions are not permitted within 14 days of platelet assessment * Total bilirubin ≤ 1.5 X upper limit of normal (ULN) * Aspartate aminotransferase (AST) ≤ 3.0 x ULN * Alanine aminotransferase (ALT) ≤ 3.0 x ULN * Creatinine clearance of ≥ 30 mL/min per 24 hour urine test or the Cockcroft-Gault formula * 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 6 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) Exclusion Criteria: * Patient planned to stop pembrolizumab at time of referral for SBRT * Vaccination with live attenuated vaccines within 4 weeks of study agent administration except forthcoming coronavirus disease 2019 (COVID-19) and flu vaccines * Subject is currently using or has used immunosuppressive medication within 14 days prior to the study agent administration with the exception of: * Intranasal, topical, inhaled, or local steroid injections (e.g., intra-articular injection) * Chronic systemic corticosteroids at physiologic doses not to exceed 5 mg/day of prednisone or equivalent * Steroids as premedication for hypersensitivity reactions (e.g., infusion-related reactions, CT scan premedication) * History of allergic reactions attributed to compounds of similar chemical or biologic composition to study agent * Clinically significant uncontrolled illness * Infection requiring systemic antibiotic therapy within 14 days prior to start of study treatment * Patient unable to tolerate PET scan even with anxiolytic medications * Other active metastatic malignancy. Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial * Females only: Pregnant or breastfeeding * Any other condition that would, in the Investigator's judgment, contraindicate the patient's participation in the clinical study due to safety concerns with clinical study procedures * Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)