Phase I Evaluation of Immunotoxin LMB-100 Administered by Normothermic, Intrapleural Perfusion Following Cytoreductive Surgery in Participants With Pleural Mesotheliomas, or Pleural Effusions From Cancers Expressing Mesothelin

-INCLUSION CRITERIA: 1. Histologically confirmed by the Laboratory of Pathology (LP), CCR, NCI mesothelinpositive malignancy arising from or metastatic to the pleura that is potentially amenable to cytoreductive surgery (R0-R2) and subsequent intrapleural perfusion based on standard of care (SOC) imaging. 2. Participants with biphasic MPM must have a \< 50% sarcomatoid component. 3. Participants with MPE from extra-thoracic disease may be eligible provided these sites are controlled and are less threatening than the pleural involvement LENT score \>=2 . 4. Participants with stage IV cancers affecting the pleura with MPE must have received firstline standard of care systemic treatment for their malignancies. 5. MPM participants must not have received any local or systemic therapy for their disease. 6. All acute toxic effects of any prior radiotherapy, chemotherapy, or surgical procedure must have resolved to Grade \<= 1 except hemoglobin (Hgb) \<= Grade 2, alopecia (any grade), and \<= Grade 2 peripheral neuropathy. 7. Age \>18 years. 8. ECOG performance status of \< 2. 9. Participants must have adequate pulmonary reserve evidenced by post-operative predicted FEV1 and adjusted DLCO \>= 40% predicted. 10. Room air oxygen saturation \>= 90%; otherwise pCO2 \<= 45 and pO2 \>= 60 on room air arterial blood gas (ABG). 11. Adequate organ and marrow function as defined below: * leukocytes \>= 3,000/mcL * absolute neutrophil count \>= 1,500/mcL (without transfusion or cytokine support) * absolute lymphocyte count \> 800/mcL * platelets \>= 100,000/mcL * Hgb \>= 9 g/ dL (with transfusion if necessary, within 1 week prior to treatment) * serum albumin \>= 2.0 mg/dL * AST/ALT \<= 2.5 X institutional ULN * creatinine clearance (eGFR) \>= 50 mL/min/1.73 m\^2 by Cockcroft-Gault formula * INR \<= 1.5 x ULN * TSH, T3 and T4 within normal limits (WNL) per institutional criteria * random serum cortisol within normal limits (WNL) per institutional criteria * total bilirubin \< 1.5 X institutional ULN (excluding Gilbert s Syndrome) 12. No active brain metastases. Participants with a history of brain metastases except those with meningeal carcinomatosis or leptomeningeal disease may be eligible for treatment a minimum of 1 week following completion of gamma knife or whole-brain radiotherapy, or 4 weeks following surgical resection of brain metastases provided post-treatment MRI scan reveals no evidence of active disease and no ongoing need for systemic steroids. 13. Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) at the study entry, for the duration of study treatment and up to 4 months (women) or 2 months (men) after the last dose of the study drug. 14. Breastfeeding participants must be willing to discontinue breastfeeding from study enrollment through two months after the LMB-100 perfusion. 15. HBV-infected participants must be on antivirals and have HBV DNA \<100 IU/mL. HCV-infected participants can be enrolled if HCV RNA level is undetectable. 16. The ability of the participant to understand and the willingness to sign a written informed consent. 17. Participants must be enrolled into protocol 06C0014 "Prospective Evaluation of Genetic and Epigenetic Alterations in Patients with Thoracic Malignancies". 18. Participants must provide acceptable archival tumor samples or have at least 1 focus of disease that is amenable to tumor biopsy if necessary for confirmation of histology, and assessment of mesothelin expression. EXCLUSION CRITERIA: 1. Active smokers. 2. Participants receiving systemic steroids other than physiologic replacement doses or inhaled corticosteroids (\<= 20 mg of dexamethasone a day \[or equivalent\]) for \<= 7 consecutive days prior to treatment initiation). 3. Treatment with chemotherapy, targeted therapy, immunotherapy, radiation, or surgery to an index lesion within three weeks prior to commencing protocol therapy, excluding minor surgical procedures (i.e. VATS/thoracentesis/PleurX catheter placement to palliate MPE). 4. Treatment with another investigational agent within four weeks prior to commencing protocol therapy. 5. History of allergic reactions attributed to compounds of chemical or biologic composition similar to LMB-100 or SS1P including pseudomonas endotoxin. 6. Clinically significant cardiovascular/cerebrovascular disease as follows: cerebral vascular accident/stroke (within 6 months prior to treatment initiation) or myocardial infarction (within 6 months prior to treatment initiation) unless revascularized, unstable angina, congestive heart failure (New York Heart Association Classification Class \>= II), serious cardiac arrhythmia, abnormal ejection fraction (echocardiogram \[ECHO\]) \<= 40%, clinically significant bleeding or clinically significant pulmonary embolism. 7. History of pneumonitis (idiopathic or drug-induced) unless cleared by pulmonary consultants. 8. Receipt of any organ transplantation, including allogeneic stem-cell transplantation, except transplants that do not require immunosuppression (e.g., corneal transplant, hair transplant). 9. HIV-infected participants. Participants on stable doses of antiretroviral therapy whose HIV RNA is below level of quantification are eligible. 10. Active COVID-19 infection. 11. Active infections requiring systemic therapy. 12. An additional malignancy that is progressing or requires active treatment. 13. Pregnancy 14. Uncontrolled intercurrent illness or psychiatric illness/social situations that would limit compliance with study requirements.