Labyrinthin Vaccination in Veterans With Lung Adenocarcinoma

Inclusion Criteria: * Ability to understand and willingness to sign an informed consent form * Histologically confirmed diagnosis of lung adenocarcinoma * Subjects with advanced/metastatic or recurrent solid tumors, with measurable or non-measurable disease as determined by Response Evaluation Criteria In Solid Tumors (RECIST) version 1.1 are eligible for participation. * Histologically confirmed diagnosis of labyrinthin-positive lung adenocarcinoma * Received at least one line of anti-PD-1 or anti-PD-L1 therapy for any stage of non-Small Cell Lung Cancer (NSCLC). Anti-PD-1 or anti-PD-L1 may have been given alone or in combination with other therapy * Progressed on at least one line of therapy if participant has a known sensitizing mutation for which an FDA-approved targeted therapy for NSCLC exists (e.g., EGFR, ALK, ROS1, BRAF, RET, NTRK, and MET sensitizing mutations) * All subjects must be candidates for pembrolizumab therapy * Subjects can either have progressed, had no response, or intolerance to prior cancer therapy. Patients must have recovered from all clinically significant treatment-related toxicities to grade 1 or less, except chemotherapy-associated peripheral neuropathy (motor or sensory), or endocrine-related AE, in which recovery to ≤ Grade 2 is allowed. For endocrine-related AEs, physiological doses of replacement therapy (e.g., levothyroxine, insulin, hydrocortisone, or other replacement therapy for adrenal or pituitary insufficiency, etc.) are allowed. * No limit on prior lines of therapy for metastatic disease. Prior chemotherapy, immunotherapy (including pembrolizumab) or molecularly targeted therapy must have been completed at least 3 weeks prior to initiating study treatment. Prior palliative radiation must have been completed at least 2 weeks prior to initiating study treatment. * Subjects with known untreated, active brain and/or leptomeningeal metastases are excluded. Subjects with treated brain metastasis who are neurologically stable and off steroids for at least one week are eligible. * Eastern Cooperative Oncology Group (ECOG) performance status of 0-1 * Life expectancy of ≥ 6 months at the time of initiating study treatment * Subjects must demonstrate adequate organ function as defined below: * Absolute neutrophil count (ANC) greater than or equal to 1,000 cells /Liter (L) * Absolute lymphocyte counts (ALCs) greater than or equal to 600 cells per microliter * Platelets greater than or equal to 75,000 cells/L * Creatinine clearance as calculated per Cockcroft-Gault or Modification of Diet in Renal Disease (MDRD) formula ≥30 milliliters(mL)/minute (min) * Total bilirubin ≤ 1.5 times the upper limit of normal (ULN), OR direct bilirubin ≤ ULN for participants with total bilirubin levels \>1.5 times the ULN * Aspartate aminotransferase or serum glutamic-oxaloacetic transaminase (AST or SGOT) and alanine aminotransferase or serum glutamic-pyruvic transaminase (ALT or SGPT) ≤2.5 times the ULN, OR ≤5 times the ULN for participants with liver metastases * Because the effects of the study treatment on the unborn fetus or nursing infant are unknown, pregnant and nursing women are ineligible. Women of childbearing age must have a negative urine or serum pregnancy test-Human Chorionic Gonadotropin(HCG) within 72 hours prior to receiving the first dose of study medication. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. * Confirmation of adequate archival tumor specimens (i.e., sufficient specimens for ten, 5-7 micrometer (µm) thick, unstained sections) Exclusion Criteria: * Subjects who have autoimmune diseases that require immunosuppressive medications other than prednisone ≤ 10 milligram (mg) daily or equivalent. Physiological doses of replacement therapy (e.g., levothyroxine, insulin, hydrocortisone, or other replacement therapy for adrenal or pituitary insufficiency, etc.) are not considered a form of immunosuppressant and are allowed. * Prior splenectomy * Pregnant or nursing women * Any medical condition including additional malignancies, laboratory abnormalities, or psychiatric illness that in the opinion of the investigator would prevent the subject from participating and adhering to study related procedures. * Uncontrolled concomitant disease that in the opinion of the investigator would interfere with the subject's safety or compliance on trial * Severe infection that in the opinion of the investigator would interfere with subject safety or compliance on trial within 4 weeks prior to enrollment * Subjects who have contraindications to GM-CSF injections according to the package insert (e.g., subjects with excessive leukemic myeloid blasts in the bone marrow or peripheral blood (≥ 10%); known hypersensitivity to GM-CSF, yeast-derived products or any component of the product) Additional exclusion criteria for participants entering Phase 2: * Is receiving systemic steroid therapy (\> 10 mg prednisone oral daily or equivalent) or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment * Has a known history of active TB (Bacillus Tuberculosis) * Hypersensitivity to pembrolizumab or any of its excipients * Has had a prior anti-cancer monoclonal antibody (mAb) within 3 weeks prior to study Day 1 or who has not recovered (i.e., ≤ Grade 1 or at baseline) from adverse events due to agents administered more than 3 weeks earlier * Has had prior chemotherapy, targeted therapy, or radiation therapy within 2 weeks prior to study Day 1 or who has not recovered (i.e., ≤ Grade 1 or at baseline) from adverse events due to a previously administered agent Note: Subjects with ≤ Grade 2 neuropathy are an exception to this criterion and may qualify for the study. Note: If subjects received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy. * Has known untreated, symptomatic central nervous system (CNS) metastases and/or carcinomatous meningitis. Subjects with previously treated brain metastases may participate provided they are stable (without evidence of progression by imaging for at least four weeks prior to the first dose of trial treatment and any neurologic symptoms have returned to baseline), have no evidence of new or enlarging brain metastases requiring treatment, and are not using steroids (\> 10 mg prednisone oral daily or equivalent) for at least 7 days prior to trial treatment. This exception does not include carcinomatous meningitis which is excluded regardless of clinical stability. * Has known history of ≥ grade 3 pneumonitis or interstitial lung disease related to radiation, immunotherapy, chemotherapy, or targeted therapy * Has an active infection requiring systemic therapy * Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator * Has known active Hepatitis B (e.g., Hepatitis B Surface Antigen (HBsAg) reactive) or Hepatitis C (e.g., HCV RNA \[qualitative\] is detected) * Has received a live vaccine within 30 days of planned start of study therapy Note: Seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however intranasal influenza vaccines (e.g., Flu-Mist®) are live attenuated vaccines, and are not allowed. Corona Virus Disease (COVID) vaccines are allowed.