Anti-Mesothelin Immunotoxin LMB-100 Followed by Pembrolizumab in Malignant Mesothelioma

* INCLUSION CRITERIA: Participants are eligible to be included in the study only if all of the following criteria apply. * Male and female participants who are at least 18 years of age on the day of signing the informed consent will be enrolled in the study. * Subjects must have histologically confirmed diagnosis of: * Cohort 1: Histologically confirmed epithelial or biphasic pleural mesothelioma (with \<50% sarcomatoid component) not amenable to potentially curative surgical resection. The diagnosis will be confirmed by the Laboratory of Pathology, Center for Cancer Research (CCR), National Cancer Institute (NCI). OR * Cohort 2: Histologically confirmed epithelial or biphasic peritoneal mesothelioma (with \<50% sarcomatoid component) not amenable to potentially curative surgical resection. The diagnosis will be confirmed by the Laboratory of Pathology, CCR, NCI. * Have provided archival tumor tissue sample or newly obtained core or excisional biopsy of a tumor lesion not previously irradiated. Formalin-fixed, paraffin embedded (FFPE) tissue blocks are preferred to slides. Newly obtained biopsies are preferred to archived tissue. Note: If submitting unstained cut slides, newly cut slides should be submitted to the testing laboratory within 14 days from the date slides are cut. * Have measurable disease based on Response Evaluation Criteria in Solid Tumors (RECIST) 1.1. Lesions in a previously irradiated area are considered measurable if progression has been demonstrated in such lesions. * Subjects must have at least one prior chemotherapy regimen that includes pemetrexed and cisplatin or carboplatin. * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. Evaluation of ECOG is to be performed within 7 days prior to start of study therapy. * Have adequate organ and marrow function as defined below: * Hematological- hemoglobin: \>= 9 g/dL or \>= 5.6 mmol/L(a) * Hematological- absolute neutrophil count: \>= 1,500/mcL * Hematological- platelets: \>= 100,000/mcL * Hepatic- total bilirubin: less than or equal to 2.5 X institutional upper limit of normal (ULN) OR direct bilirubin less than or equal to ULN for participants with total bilirubin levels \>1.5 X ULN * Hepatic- aspartate aminotransferase (AST) and alanine aminotransferase (ALT): less than or equal to 2.5 X institutional ULN (less than or equal to 5 X ULN for participants with liver metastases) * Renal-Creatinine less than or equal to 1.5 x ULN OR \>= 50 mL/min for participant with creatinine levels \> 1.5 X institutional ULN. Measured or calculated(b) creatinine clearance (Glomerular filtration rate (GFR) can also be used in place of creatinine or creatinine clearance (CrCl) * Coagulation-International normalized ratio (INR) OR prothrombin time (PT)/ Activated partial thromboplastin time (aPTT): less than or equal to 1.5 x ULN unless participant is receiving anticoagulant therapy as long as PT or aPTT is within therapeutic range of intended use of anticoagulants * ALT (SGPT)=alanine aminotransferase (serum glutamic pyruvic transaminase); * AST (SGOT)=aspartate aminotransferase (serum glutamic oxaloacetic transaminase); * GFR=glomerular filtration rate; ULN=upper limit of normal. * a. Criteria must be met without erythropoietin dependency and without packed red blood cell (pRBC) transfusion within last 2 weeks. * b. Creatinine clearance (CrCl) or estimated glomerular filtration rate (eGFR) should be calculated per institutional standard. * Must have left ventricular ejection fraction \>50%. * Must recovered from all adverse events (AEs) due to previous therapies to less than or equal to Grade 1 or baseline. Participants with less than or equal to Grade 2 neuropathy may be eligible. If participant received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting study treatment. * Must have recovered from all radiation-related toxicities, not require corticosteroids, and not have had radiation pneumonitis. A 1-week washout is permitted for palliative radiation (less than or equal to 2 weeks of radiotherapy) to non-central nervous system (CNS) disease. * If participant received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting study treatment. * The effects of LMB-100 on the developing human fetus are unknown. For this reason and because anti-programmed cell death protein 1 (PD-1) antibodies such as pembrolizumab are assumed to be teratogenic: * A male participant must agree to use contraception during the treatment period and for at least 180 days after the last dose of study treatment and refrain from donating sperm * A female participant is eligible to participate if she is not pregnant, not breastfeeding, and at least one of the following conditions applies: * Not a woman of childbearing potential (WOCBP) OR * A WOCBP who agrees to follow the contraceptive guidance in Appendix B during the treatment period and for at least 180 days after the last dose of study treatment. * 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. * The participant provides written informed consent for the trial. EXCLUSION CRITERIA: \- Is currently participating in or has participated in a study of an investigational agent or has used an investigational device within 4 weeks prior to the first dose of study treatment. Note: Participants who have entered the follow-up phase of an investigational study may participate as long as it has been 4 weeks after the last dose of the previous investigational agent. * Has known active CNS metastases and/or carcinomatous meningitis. Participants with previously treated brain metastases may participate provided they are radiologically stable, i.e. without evidence of progression for at least 4 weeks by repeat imaging (note that the repeat imaging should be performed during study screening), clinically stable and without requirement of steroid treatment for at least 14 days prior to first dose of study treatment. * Has severe hypersensitivity (\>= Grade 3) to pembrolizumab, LMB-100 and/or any of their excipients. * Subjects who have received prior therapy with LMB-100, an anti-PD-1, anti-PD-L1, or anti-programmed cell death ligand 2 (PD-L2) agent or with an agent directed to another stimulatory or co-inhibitory T-cell receptor (e.g., Cytotoxic T-lymphocyte antigen 4 (CTLA-4), OX-40, tumor necrosis factor receptor superfamily member 9 (CD137). * Has received prior systemic anti-cancer therapy including investigational agents within 4 weeks prior to start of study therapy. * Has received prior radiotherapy within 2 weeks of start of study treatment. * Has had a prior pneumonectomy * Has received a live vaccine within 30 days prior to the first dose of study drug. Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster (chicken pox), yellow fever, rabies, Bacillus Calmette-Guerin (BCG), and typhoid vaccine. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (e.g., FluMist(R)) are live attenuated vaccines and are not allowed. * Has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy (in dosing exceeding 10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior to start of study therapy. * Has active autoimmune disease that has required systemic treatment in the past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (e.g.., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment. * Has a history of (non-infectious) pneumonitis/interstitial lung disease (ILD) that required steroids or has current pneumonitis/ILD * Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study, interfere with the subject's participation for the full duration of the study, or is not in the best interest of the subject to participate, in the opinion of the treating investigator. * Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial. * A WOCBP who has a positive urine pregnancy test within 72 hours prior to start of study therapy (see Appendix B). If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. Note: in the event that 72 hours have elapsed between the screening pregnancy test and the first dose of study treatment, another pregnancy test (urine or serum) must be performed and must be negative in order for subject to start receiving study medication. * Is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the study, starting with the screening visit through 180 days after the last dose of trial treatment. Pregnant women are excluded from this study because LMB-100 + pembrolizumab are agents with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with LMB-100 + pembrolizumab, breastfeeding should be discontinued if the mother is treated with LMB-100 + pembrolizumab. These potential risks may also apply to other agents used in this study. * Has a known history of Human Immunodeficiency Virus. HIV positive patients will be excluded due to a theoretical concern that the degree of immune suppression associated with the treatment may result in progression of HIV infection. (Note: No HIV testing is required) * Has a known history of Hepatitis B (defined as Hepatitis B surface antigen \[HBsAg\] reactive) or known active Hepatitis C virus (defined as HCV ribonucleic acid (RNA) \[qualitative\] is detected) infection. or active hepatitis B virus (HBV) or HCV infection. (Note: No testing for Hepatitis B and Hepatitis C is required.) * Has a known additional malignancy that is progressing or has required active treatment within the past 2 years. Note: Participants with basal cell carcinoma of the skin, squamous cell carcinoma of the skin, or carcinoma in situ (e.g. breast carcinoma, cervical cancer in situ) that have undergone potentially curative therapy are not excluded. * Has an active infection requiring systemic therapy.