A Clinical Study of the Safety and Effectiveness of an Investigational Cell Therapy Given With and Without an Investigational RNA-based Vaccine in Patients With Organ Tumors

Inclusion Criteria: * Each patient enrolled in the trial must have CLDN6-positive tumor regardless of tumor histology defined as ≥ 50% of tumor cells expressing CLDN6 protein at an intensity of ≥2+ using a semi-quantitative immunohistochemistry assay in a central laboratory for specific detection of CLDN6 protein expression in formalin-fixed, paraffin-embedded (FFPE) neoplastic tissues. * Availability of a FFPE tumor tissue sample. FFPE sample can be from an archival tumor tissue sample. It should be from the most recent tumor tissue obtained and must not be \>3 years old. If an archival sample is not available, the patient must be biopsied for CLDN6 staining. If an archival tumor sample is ≤3 years old but the patient has received a treatment that may influence expression of CLDN6 after the archival tumor sample was obtained, a fresh tumor biopsy is required. * Must have histological documentation of the original primary tumor via a pathology report. * Must have measurable disease per RECIST v1.1 (except for germ cell tumors, where patients can be evaluated according to Cancer-Antigen (CA)-125, Alpha-fetoprotein or beta-human chorionic gonadotropin (βhCG) \[as applicable\], or ovarian cancer, where patients can be evaluated according to CA-125. The pre-treatment sample must be at least twice the upper limit of normal). * Must have a histologically confirmed solid tumor that is metastatic or unresectable and for which there is no available standard therapy likely to confer clinical benefit, or the patient is not a candidate for such available therapy. * Must be ≥ 18 years of age at the time the pre-screening informed consent is signed. * Must sign an informed consent form indicating that he or she understands the purpose of and procedures required for the trial and are willing to participate in the trial prior to any trial-related assessments or procedures. * Must have an Eastern Cooperative Oncology Group performance status of 0 to 1. * Must have adequate coagulation function at screening as defined in the protocol. * Must have adequate hematologic function at screening as defined in the protocol. * Must have adequate hepatic function at screening as defined in the protocol. * Must have adequate renal function at screening as defined in the protocol. * Must be able to attend trial visits as required by the protocol. * Women of childbearing potential (WOCBP) must have a negative serum (βhCG) test/value at screening. Patients who are post-menopausal or permanently sterilized can be considered as not having reproductive potential. * WOCBP must agree not to donate eggs (ova, oocytes) for the purposes of assisted reproduction during the entire trial and thereafter. * WOCBP and men who are sexually active with a WOCBP and have not had a vasectomy must agree to use highly effective birth control method(s), as defined in the protocol. True abstinence is an acceptable alternative to the use of contraception. * Men must agree not to father a child or donate sperm, and WOCBP must agree not to become pregnant during the trial and for at least 12 months after the CLDN6 CAR-T infusion or CLDN6 RNA-LPX treatment. For Part 2 only: * Histologically or cytologically confirmed solid tumor fulfilling inclusion criteria 1-4 that is metastatic or unresectable, and for whom there is no available standard therapy likely to confer clinical benefit, or patient who is not a candidate for such available therapy. Exclusion Criteria: * Has received prior CAR-T therapy, except CLDN6 CAR-T therapy. * Has received vaccination with live virus vaccines within 6 weeks prior to the start of lymphodepletion (LD). * Receives concurrent systemic (oral or i.v.) steroid therapy \>10 mg prednisolone daily, or its equivalent, for an underlying condition. * Has side effects of any prior therapy or procedures for any medical condition not recovered to National Cancer Institute Common Terminology Criteria for Adverse Avents version 5.0 Grade ≤1. Medical conditions: * Current evidence of new or growing brain or spinal metastases during screening. Patients with known brain or spinal metastases may be eligible if they: 1. Have had radiotherapy or another appropriate therapy for the brain or spinal metastases. The therapy must be completed at least 3 weeks prior to CLDN6 CAR-T administration, 2. Have no neurological symptoms, 3. Have stable brain or spinal disease on the computer tomography or magnetic resonance imaging scan within 3 weeks before CLDN6 CAR-T administration, 4. Are not undergoing acute corticosteroid therapy or steroid taper. Chronic steroid therapy is acceptable provided that the dose is stable for the last 14 days prior to screening (≤10 mg prednisolone daily or equivalent), 5. Do not require steroid therapy within 7 days before the first dose of CLDN6 CAR-T, and 6. Do not have anticipated imminent fracture or cord compression due to spinal bone metastases. * Has history of epilepsy. Isolated seizures in the past or febrile seizures in childhood are permitted; has a history of a cerebrovascular accident or transient ischemic attack less than 6 months ago. * Pericardial effusion requiring any drainage is excluded. * Has an active autoimmune disease including but not limited to inflammatory bowel disease, systemic lupus erythematosus, ankylosing spondylitis, scleroderma, or multiple sclerosis. Has any active immunologic disorder requiring immunosuppression with steroids or other immunosuppressive agents with the exception of patients with isolated vitiligo, resolved childhood asthma or atopic dermatitis, controlled hypoadrenalism or hypopituitarism, and euthyroid patients with a history of Grave's disease. Patients with controlled hyperthyroidism must be negative for thyroglobulin, thyroid peroxidase antibodies, and thyroid-stimulating immunoglobulin prior to trial drug administration. * Seropositivity for human immunodeficiency virus. * Known history/positive serology for hepatitis B requiring active antiviral therapy (unless immune due to vaccination or resolved natural infection or unless passive immunization due to immunoglobulin therapy). Patients with positive serology must have hepatitis B virus viral load below the limit of quantification. * Active hepatitis C virus (HCV) infection; patients who have completed curative antiviral treatment with HCV viral load below the limit of quantification are allowed. * Has a known hypersensitivity to a component of CLDN6 CAR-T or the CLDN6 RNA-LPX drug product, or another similar compound. * History of severe immediate hypersensitivity reaction to LD chemotherapy consisting of cyclophosphamide or fludarabine. * Has a history of another primary cancer within the 2 years prior to enrollment except for the following: Non-melanoma skin cancer, cervical carcinoma in situ, superficial bladder cancer, prostate cancer with currently undetectable prostate specific antigen, or other non-metastatic carcinoma that has been in complete remission without treatment for more than 2 years. * Receipt of allogenic stem cell transplantation in the 5 years prior to enrollment into the trial. * Patients with acute or chronic graft versus host disease. Other comorbidities: * Has abnormal electrocardiograms that are clinically significant, such as QT prolongation. * In the opinion of the investigator, has any concurrent conditions that could pose an undue medical hazard or interfere with the interpretation of the trial results; these conditions include, but are not limited to: 1. Ongoing or active infection requiring antibiotic/antiviral/antifungal therapy 2. Concurrent congestive heart failure (New York Heart Association Functional Classification Class III or IV) 3. Concurrent unstable angina 4. Concurrent cardiac arrhythmia requiring treatment 5. Acute coronary syndrome within the previous 6 months 6. Significant pulmonary disease (shortness of breath at rest or on mild exertion) for example due concurrent severe obstructive pulmonary disease. * Has a cognitive, psychological or psychosocial impediment that would impair the ability of the patient to receive therapy according to the protocol or adversely affect the ability of the patient to comply with the informed consent process, protocol, or protocol-required visits and procedures. * Is pregnant or breastfeeding. Disease-specific exclusion criteria: * Have a pure βhCG-secreting germ cell tumor.