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

This phase I trial studies the side effects and best dose of COH06 with or without atezolizumab in patients with non-small cell lung cancer previously treated with PD-1 and/or PD-L1 immune checkpoint inhibitors that has spread to other places in the body (advanced) and that has not responded to previous treatment (refractory). NK cells are infection fighting blood cells that can kill tumor cells. The NK cells given in this study, COH06, will come from umbilical cord blood and will have a new gene put in them that makes them express PD-L1, and express and secrete IL-15. NK cells that express PD-L1 may kill more tumor cells, and IL-15 may allow the NK cells to live longer. Immunotherapy with monoclonal antibodies, such as atezolizumab, may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. Giving COH06 without or without atezolizumab may help control the disease in patients with non-small cell lung cancer.

PRIMARY OBJECTIVES:

I. Assess the safety and determine the optimal biological dose (OBD) of COH06 as monotherapy and when given in combination with atezolizumab (Atezo).

II. Assess the cellular kinetics of COH06 through the detection and measurement of persistence in the peripheral blood.

SECONDARY OBJECTIVES:

I. Estimate overall response (complete response \[CR\] + partial response \[PR\]) and disease control (CR + PR + stable disease \[SD\]) rates, including duration.

II. Estimate the progression free survival (PFS) and overall survival (OS) rate, at 6-months and 1-year post (first) COH06 cell infusion.

CORRELATIVE STUDY OBJECTIVES:

I. Assess the phenotype and activation status of COH06 via flow cytometry, polymerase chain reaction (PCR), and cytokine analysis.

II. Assess T cell activation by flow cytometry and cytokine analysis.

OUTLINE: This is a phase I dose-escalation study of COH06.

Patients receive fludarabine intravenously (IV) on days -5 to -3, cyclophosphamide IV on days -5 to -3, and COH06 IV on days 0, 7, 14, and 21 in the absence of disease progression or unacceptable toxicity. Patients assigned to dose level 4 also receive atezolizumab IV over 60 minutes on days 0, 14, 28, and 42 in the absence of disease progression or unacceptable toxicity.

After completion of the study treatment, patients are followed for 30 days, every 8 weeks until disease progression, and then annually for 15 years.

Eligibility Criteria:
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)