Adjuvant Tumor Lysate Vaccine and Iscomatrix With or Without Metronomic Oral Cyclophosphamide and Celecoxib in Patients With Malignancies Involving Lungs, Esophagus, Pleura, or Mediastinum

-INCLUSION CRITERIA: 1. Patients with histologically or cytologically proven lung or esophageal cancers, thymic or mediastinal germ cell tumors, malignant pleural mesotheliomas, or primary thoracic sarcomas, as well as patients with sarcomas, melanomas, germ cell tumors, or epithelial malignancies metastatic to the lungs, mediastinum, or pleura that have no clinical evidence of active disease (NED) or minimal residual disease (MRD) not readily accessible by non-invasive biopsy or resection/radiation following standard therapy. 2. Diagnosis must be confirmed by the National Cancer Institute (NCI) Laboratory of Pathology. 3. Patients must be enrolled within 56 weeks following completion of therapy. 4. Patients must have completed standard therapy for their malignancy and recovered from all toxicities to less than or equal to Grade 2 within 3 weeks prior to enrollment. 5. Patients with intracranial metastases, which have been treated by surgery or radiation therapy, may be eligible for study provided there is no evidence of active disease and no requirement for anticonvulsant therapy or steroids following treatment. 6. Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 - 2 7. Patients must be 18 years of age or older due to the unknown effects of immunologic responses to this vaccine during childhood and adolescent development. 8. Patients must have evidence of adequate bone marrow reserve, hepatic and renal function as evidenced by the following laboratory parameters: * Absolute neutrophil count greater than 1500/mm\^3 * Platelet count greater than 100,000/mm\^3 * Hemoglobin greater than 8g/dl (patients may receive transfusions to meet this parameter) * Prothrombin (PT) within 2 seconds of the upper limit of normal (ULN) * Total bilirubin \<1.5 x upper limits of normal * Serum creatinine less than or equal to 1.6 mg/ml or the creatinine clearance must be greater than 70 ml/min/1.73m\^2. 9. Seronegative for human immunodeficiency virus (HIV) antibody. Note: The experimental treatment being evaluated in this protocol depends on an intact immune system. Patients who are HIV seropositive may have decreased immune competence and thus may be less responsive to the experimental treatment. 10. Seronegative for active hepatitis B, and seronegative for hepatitis C antibody. If hepatitis C antibody test is positive, then patient must be tested for the presence of antigen by reverse transcription polymerase chain reaction (RT-PCR) and be hepatitis C virus (HCV) ribonucleic acid (RNA) negative. 11. The effects of the study treatment on the developing human fetus are unknown; thus, women of childbearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) within 28 days prior to study entry, for the duration of study participation and up to 120 days after the last dose of the drug. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. 12. Patients must be willing to sign an informed consent. 13. Ability and willingness to co-enroll on the screening and tissue collection protocol 06C0014, 'Prospective Evaluation of Genetic and Epigenetic Alterations in Patients with Thoracic Malignancies'. EXCLUSION CRITERIA: 1. Patients who are initially rendered no clinical evidence of active disease (NED) or have minimal residual disease (MRD) following standard therapy but exhibit disease progression prior to initiation of vaccination will be excluded from the study. 2. Patients requiring chronic systemic treatment with steroids will be excluded. 3. Patients receiving warfarin anticoagulation, who cannot be transitioned to other agents such as enoxaparin or dabigatran, and for whom anticoagulants cannot be held for up to 24 hours will be excluded. 4. Patients with uncontrolled hypertension (\>160/95), unstable coronary disease evidenced by uncontrolled arrhythmias, unstable angina, decompensated congested heart failure (CHF) (\>New York Heart Association (NYHA) Class II), or myocardial infarction within 6 months of study will be excluded. 5. Patients with other cardiac diseases may be excluded at the discretion of the PI following consultation with Cardiology consultants. 6. Patients with any of the following pulmonary function abnormalities will be excluded: forced expiratory volume (FEV), \< 30% predicted; carbon monoxide (DLCO) \< 30% predicted (post-bronchodilator); oxygen saturation less than 92% on room air. 7. Female patients who are pregnant or breastfeeding. Because there is unknown, potentially harmful effects of immune response to CT-X antigens and stem cell proteins that may be expressed in placenta, fetus, and neonates. 8. Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations 3 months prior to enrollment that would limit compliance with study requirements.