Evaluation of a Cancer Lysate Vaccine and Montanide (Registered Trademark) ISA-51 VG With or Without the IL-15 Super-Agonist N-803 as Adjuvant Therapy for PD-L1 Negative Non-Small Cell Lung Cancer

Background: * Cancer-testis (CT) antigens (CTA), particularly those encoded by genes on the X chromosome (CT-X antigens) have emerged as attractive targets for cancer immunotherapy. * Recent studies suggest that CT-X antigens which are up regulated by epigenetic mechanisms may be preferentially expressed in pluripotent stem/tumor initiating cells that mediate treatment resistance and metastasis of human cancers. * Whereas pulmonary malignancies express a variety of CT-X antigens, immune responses to these proteins are uncommon in lung cancer patients due to low-level, heterogeneous antigen expression, epigenetic repression of genes regulating antigen processing/presentation, and local as well as systemic immunosuppression in these individuals. * Conceivably, vaccination of lung cancer patients with tumor cells expressing high levels of CT-X antigens in combination with regimens that inhibit immunosuppressive functions of T regulatory cells and enhance activity of natural killer (NK) cells will induce broad immunity to these antigens. Primary Objectives: * Phase I Component: To determine the safety of H1299 lung cancer cell lysate vaccines administered with Montanide (Registered Trademark) ISA-51 VG adjuvant and N-803. * Phase II Component: To assess the frequency of immunologic responses to purified CT-X and autosomal CT antigens in NSCLC participants following vaccinations with H1299 cancer cell lysate and Montanide (Registered Trademark) ISA-51 VG adjuvant in combination with N-803. Eligibility: * Participants with pathologically confirmed Stage IB-IIIA (T2a-T4/N0, T1-T3N1, T1-T2/N2) NSCLC per 8th edition TNM Staging System non-small cell lung cancer (NSCLC) who have no clinical evidence of active disease (NED) following standard therapy completed within the past 12 weeks. * Participants must be 18 years or older with an ECOG performance status of 0-2. * Participants must have adequate bone marrow, kidney, liver, lung, and cardiac function. * Participants receiving systemic immunosuppressive medications will be excluded. * Participants with HIV will be excluded. Design: * Following recovery from surgery, and adjuvant therapy if indicated, eligible participants will be vaccinated via deep subcutaneous (SQ) injection with H1299 cell lysate and Montanide (Registered Trademark) ISA-51 VG (Trademark) adjuvant with or without subcutaneous N-803 monthly until six vaccinations have been given. * Imaging studies will be performed at baseline, one month following the 3rd and 6th vaccinations, and at post-treatment follow-up (every 3 months for 3 years and then every 6 months for another 2 years, for 5 years total follow-up). * Leukapheresis will be performed at baseline and at treatment evaluation one month following completion of the six vaccinations. * Systemic toxicities and immunologic responses to therapy will be recorded. * Pre- and post-vaccination serologic and cell mediated responses to a panel of CT-X antigens will be assessed before and one month following completion of the six vaccinations. * Individuals deemed to have responded to vaccine treatment and exhibit no evidence of disease recurrence or secondary malignancy will be eligible for 2 additional vaccinations at 3 months after receiving the sixth vaccine and 6 months after receiving the 6th vaccine with N-803. * Numbers and percentages of immune subsets, soluble factors, and cytokines in peripheral blood will be assessed before and after the six vaccinations. * Immunologic responses to autologous tumor cells (if available) as well as pooled lung cancer stem cell vs. normal lung-induced pluripotent stem cell (Lu-iPSC) lysates will be evaluated in an exploratory manner. * Up to 28 participants may receive study intervention on this protocol.