Quaratusugene Ozeplasmid (Reqorsa) in Combination With Pembrolizumab in Previously Treated Non-Small Lung Cancer

Patients will have their most recent archival tumor biopsy submitted to a central laboratory for IHC analysis. Inclusion Criteria: 1. Age ≥18 years. 2. Voluntarily signed an informed consent in accordance with institutional policies. 3. Histologically or cytologically documented NSCLC (SQ, NSQ, or mixed (adenosquamous) histology) with locally advanced or metastatic disease. Note: Any level of PD-L1 TPS is allowed. 4. Achieved clinical benefit to prior pembrolizumab or pembrolizumab/platinum-based chemotherapy for at least 3 months and subsequently progressed as confirmed by radiological tumor assessment per RECIST 1.1. Patients receiving pembrolizumab as a single agent must have additional therapy with a platinum-based chemotherapy prior to enrolling, but patients receiving pembrolizumab in combination with a platinum-based chemotherapy should have enrollment in this trial as the next treatment regimen. Chemotherapy is to be limited such that study treatment will be 2nd or 3rd line. 5. For Phase 2, patients must have measurable disease per RECIST 1.1. 6. Patients with genetic alterations with FDA-approved therapy (such as EGFR or anaplastic lymphoma kinase \[ALK\] mutations) must have disease progression after treatment with appropriate targeted therapy and must be eligible for immunotherapy as determined by the investigator. 7. ECOG performance status score from 0 to 1. 8. Must be ≥28 days beyond major surgical procedures such as thoracotomy, laparotomy, or joint replacement, and must be ≥10 days beyond minor surgical procedures such as biopsy of subcutaneous tumors, pleuroscopy, etc., and must not have evidence of wound dehiscence, active wound infection, or comparable major residual complications of the surgery. Note: Placement of pleural catheter despite being a minor surgical procedure, may be performed \<10 days prior to study enrollment. 9. Demonstrate adequate organ function, as determined by the following laboratory values obtained within 21 days prior to enrollment: 1. Absolute neutrophil count (ANC) ≥1,500/μL, 2. Platelets ≥ 100,000/μL, 3. Hemoglobin ≥8.0 g/dL ≥2 weeks without transfusions, 4. International normalized ratio (INR) or prothrombin time (PT): ≤1.5 × upper limit of normal (ULN) unless the patient is receiving anticoagulant therapy as long as PT is within therapeutic range of intended use of anticoagulants, 5. Activated partial thromboplastin time (aPTT) or partial thromboplastin time (PTT): ≤1.5 × ULN unless the patient is receiving anticoagulant therapy as long as aPTT is within therapeutic range of intended use of anticoagulants, 6. Creatinine ≤1.5 × ULN OR calculated creatinine clearance (CrCl) ≥60 mL/min for patients with creatinine levels \>1.5 × ULN, 7. Serum total bilirubin ≤1.0 × ULN, 8. Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤1.5 × ULN, 9. Alkaline phosphatase ≤2.5 x ULN. 10. Stable cardiac condition with a left ventricular ejection fraction \>40% within ≤21 days prior to enrollment. 11. Asymptomatic brain metastases, must meet ALL of the following criteria (a-d): 1. No history of seizures in the preceding 6 months, 2. Definitive treatment must be completed ≥4 weeks prior to enrollment, 3. Stopped corticosteroid treatments administered because of brain metastases or related symptoms for ≥2 weeks prior to enrollment, 4. Post-treatment imaging must demonstrate stability or regression of the brain metastases. 12. Female patients of childbearing potential (FOCBP) must have a negative serum pregnancy test at screening (within 7 days of enrollment). Note: Non-childbearing potential is defined as greater than 1 year postmenopausal or surgically sterilized. 13. FOCBP and non-sterile male patients with female partner(s) of childbearing potential must agree to use 2 forms of contraception including 1 highly effective and 1 effective method beginning ≥2 weeks prior to enrollment through 4 months following the last dose of study treatment. 14. Male patients must agree to no sperm donation during study treatment and for an additional 4 months following the last dose of study treatment. Exclusion Criteria: 1. Unable to tolerate pembrolizumab treatment, leading to early treatment discontinuation or prolonged/frequent dosage modifications as determined by the investigator. 2. Hypersensitivity to docetaxel or polysorbate 80 (Phase 2 only). 3. Patients at risk of tumor lysis syndrome (e.g., renal impairment, hyperuricemia, bulky tumor \[Phase 2 randomized portion only\]). 4. Received prior systemic chemotherapy or monoclonal antibodies for the treatment of the participant's advanced or metastatic disease within 21 days of study enrollment. 5. Received prior gene therapy. 6. Received any radiotherapy to the skull, spine, thorax, or pelvis within 1 month of study enrollment. Note: Patients are permitted to have received palliative radiotherapy to an extremity provided at least 14 days has elapsed since completion of therapy, provided the patient received no more than 10 radiotherapy fractions and a dose no higher than 30 Gy to that site. 7. Expected to require any other form of antineoplastic therapy while participating in the study. 8. Received a live-virus vaccination within 1 month of enrollment. Seasonal flu vaccines that do not contain live virus are permitted. 9. Has known active, symptomatic CNS metastases and/or carcinomatous meningitis. 10. Active, known, or suspected autoimmune disease. 11. Active systemic viral, bacterial, or fungal infections(s) requiring treatment. 12. Serious concurrent illness or psychological, familial, sociological, geographical, or other condition that, in the opinion of the investigator, would prevent adequate follow-up and compliance with the study protocol. 13. A condition requiring systemic treatment with either corticosteroids (\>10 mg daily prednisone equivalents) or other immunosuppressive medications within 14 days of study enrollment. Inhaled or topical steroids and adrenal replacement doses ≤10 mg daily prednisone equivalents are permitted in the absence of active autoimmune disease. 14. Active concurrent malignancies, i.e., cancers other than NSCLC. 15. Has a second, concurrent, untreated malignancy. 16. History of symptomatic interstitial lung disease or pneumonitis that required oral (PO) or IV glucocorticoids to assist with management. Note: Lymphangitic spread of the NSCLC is not an exclusion criterion. 17. History of myocardial infarction or unstable angina within 6 months prior to enrollment. 18. Presence of pre-existing peripheral neuropathy that is ≥Grade 2 by NCI-CTCAE v5.0 criteria. 19. Is, at the time of signing informed consent, a regular user (including "recreational use") of any illicit drugs or has a recent history (within the last year) of substance abuse (including alcohol) requiring medical intervention. 20. Known human immunodeficiency virus (HIV) infection or has active hepatitis infection. 21. Female patients who are pregnant or breastfeeding.