[212Pb]VMT-Alpha-NET in Metastatic or Inoperable Somatostatin-Receptor Positive Gastrointestinal Neuroendocrine Tumors, Pheochromocytoma/Paragangliomas, Small Cell Lung, Renal Cell, and Head and Neck Cancers

* INCLUSION CRITERIA: * Participants must have histopathologically confirmed gastrointestinal neuroendocrine tumors (GI NET), pheochromocytoma/paraganglioma (PPGL), small cell lung cancers (SCLC), kidney cancers (KC), or Head \& Neck cancers (nasopharyngeal carcinoma \[NPC\], olfactory neuroblastoma \[ONB\], sinonasal neuroendocrine carcinoma \[SNEC\]) that are metastatic or inoperable per Standard of Care. Note: for KC, all histopathologies of kidney cancers are eligible as long as it is a primary renal neoplasm. * Required prior therapies: * GI NET, PPGL, H\&N: no specific prior therapy is needed. * SCLC: At least one prior line of standard of care systemic treatment such as chemotherapy and/or immunotherapy. * KC: Renal cell carcinoma (RCC) participants should have received at least one line of prior therapy in the metastatic setting and should have received at least one Programmed cell death protein 1 (PD1) / Programmed death-ligand 1 (PDL1)-targeted immune checkpoint inhibitor as well as one agent targeting the VEGF pathway. Participants with fumarate hydratase (FH) deficient RCC should have received at least one prior line of systemic therapy (such as bevacizumab plus erlotinib). No prior therapy is needed for participants with other histologic subtypes. * Have NOT received prior systemic radioligand therapy for definitive therapeutic purposes. Prior external beam radiation therapy is allowed. * History of disease progression by imaging (e.g., RECIST 1.1) or clinically (defined as increase in severity or frequency of symptoms related to disease) within the past 36 months prior to the first dose of \[203Pb\]VMT-Alpha-NET. * Evidence of somatostatin receptors (SSTR) expression on at least 50% of the radiographically identifiable (i.e., visible on an anatomic scan such as CT or magnetic resonance imaging \[MRI\]) tumor, as indicated by a positive (uptake qualitatively identifiable as above the local background) on SSTR PET scan. * Age \>= 18 years. * ECOG performance status \<=1. * Participants must have adequate organ and marrow function as defined below: * Leukocytes: 3,000/microliter * Absolute Neutrophil Count: 1,500/microliter * Platelets 100,000/microliter * Hemoglobin \>= 9.0 g/dL * Total bilirubin: within normal institutional limits. Note: \<= 5 X institutional upper limit of normal (ULN) if bilirubin elevation is due to a benign process such as Gilbert syndrome * AST: \<= 2.5 X institutional ULN * ALT: \<= 2.5 X institutional ULN * Creatinine: within normal institutional limits OR * Calculated creatinine clearance (glomerular filtration rate (eGFR): \>= 60 mL/min/1.73 m\^2 for participants with creatinine levels above institutional normal * Participants with treated brain metastases are eligible if follow-up brain imaging after central nervous system (CNS)-directed therapy shows no evidence of progression at screening. * Participants with new or progressive brain metastases or leptomeningeal disease are eligible as long as the participant is asymptomatic and not requiring medication for symptom control from the brain lesions at screening. * Participants seropositive for human immunodeficiency virus (HIV) must: * be on effective anti-retroviral therapy; and * have an undetectable viral load at screening. * Participants seropositive for hepatitis B virus (HBV), must have HBV viral load undetectable at screening. * Participants seropositive for hepatitis C virus (HCV) must: * received curative treatment; and * have an undetectable HCV viral load at screening. * Individuals of child-bearing potential (IOCBP) and individuals who can father children must agree to use an effective method of contraception (barrier, hormonal, intrauterine device \[IUD\], surgical sterilization, abstinence) at study entry and at least 6 months after the last dose of the study agent(s). * Nursing participants must be willing to discontinue nursing from study treatment initiation through 6 months after the last dose of the study agents. * The ability of the participant to understand and the willingness to sign a written informed consent document. EXCLUSION CRITERIA: * Any investigational agents should be stopped at least 28 days prior to the first dose of \[203Pb\]VMT-Alpha-NET. * Systemic therapy should be stopped at least 28 days prior to the first dose of \[203Pb\]VMT-Alpha-NET (participants with prior systemic therapies for their malignancy only, except participants with SCLC). * Systemic therapy should be stopped at least 14 days prior to the first dose of \[203Pb\]VMT-Alpha-NET (participants with SCLC only). * History of allergic reactions attributed to compounds of similar chemical or biologic composition to VMT-Alpha-NET. * Positive Beta human chorionic gonadotropin (Beta-HCG) serum or urine pregnancy test performed in IOCBP at screening. * QTc \> 450 ms on electrocardiogram (EKG) at screening. Note: Framingham correction for QTc will be used. * History of or detection at screening of active/untreated secondary malignancy except nonmelanoma skin cancer and carcinoma in situ of the uterine cervix. * Uncontrolled intercurrent illness, factors, evaluated by medical history and physical exam which would potentially increase in the risk of the participant.