Genetically Engineered Natural Killer (NK) Cells With or Without Atezolizumab for the Treatment of Non-small Cell Lung Cancer Previously Treated With PD-1 and/or PD-L1 Immune Checkpoint Inhibitors

Inclusion Criteria: * Documented informed consent of the participant and/or legally authorized representative * Assent, when appropriate, will be obtained per institutional guidelines * Agreement to allow the use of archival tissue from diagnostic tumor biopsies * Age \>= 18 years * Eastern Cooperative Oncology Group (ECOG) 0 or 1 * Lung non-small cell carcinoma (NSCLC) patients with advanced, metastatic, or recurrent disease, previously treated with a PD-1 or PD-L1 immune checkpoint inhibitor, either as single agent or in combination with chemotherapy or other immunotherapy or experimental agents * Radiographically demonstrable tumor progression treatment on or after therapy with a PD-1/PD-L1 immune checkpoint inhibitor * Preserved organ function and recovery of prior drug related toxicities (except alopecia or grade 2 anemia) to grade 1 or better * No cytotoxic chemotherapy or immunotherapy over the three weeks prior to lymphodepletion * Histologically confirmed non-small cell lung cancer * Measurable disease as per Response Evaluation Criteria in Solid Tumors (RECIST) criteria 1.1 * Fully recovered from the acute toxic effects (except alopecia) to =\< grade 1 to prior anti-cancer therapy * Absolute neutrophil count (ANC) \>= 1,500/mm\^3 * Hemoglobin (Hgb) \>= 8 g/dl * Platelets \>= 100,000/mm\^3 * Total bilirubin =\< 1.5 x upper limit of normal (ULN) * Aspartate aminotransferase (AST) =\< 1.5 x ULN * Alanine aminotransferase (ALT) =\< 1.5 x ULN * Alkaline phosphatase (AP) =\< 1.5 x ULN * Creatinine clearance of \>= 60 mL/min per 24-hour urine test or the Cockcroft-Gault formula * If not receiving anticoagulants: International normalized ratio (INR) OR prothrombin (PT) =\< 1.5 x ULN * If on anticoagulant therapy: PT must be within therapeutic range of intended use of anticoagulants * Seronegative for human immunodeficiency virus (HIV) antigen (Ag)/antibody (Ab) combo, hepatitis C virus (HCV), active hepatitis B virus (HBV) (surface antigen negative) * If positive, hepatitis C ribonucleic acid (RNA) quantitation must be performed * 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 06 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: * Autologous stem cell transplant within 1 year prior to day 1 of protocol therapy * Chemotherapy, radiation therapy, biological therapy, immunotherapy within 21 days prior to day 1 of protocol therapy * History of allergic reactions attributed to compounds of similar chemical or biologic composition to study agent * Active diarrhea * Clinically significant uncontrolled illness * Active infection requiring antibiotics * Known history and/or positive serology for immunodeficiency virus (HIV) or hepatitis B or hepatitis C infection * Diagnosis of Gilbert's disease * Other active malignancy * Females only: Pregnant or breastfeeding * Severe (grade 3 or higher) immune related adverse events during prior PD-1 inhibitor treatment * 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 * Concomitant use of other investigational agents * Patients with EGFR mutations or ALK translocations in their tumors, unless treatment with the indicated tyrosine kinase inhibitor has failed * Active brain metastases. Previously treated brain metastasis must demonstrate stability on subsequent magnetic resonance imaging (MRI) scans * 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)