INCLUSION CRITERIA:  Histologically confirmed malignant pleural or peritoneal mesothelioma not amenable to potentially curative surgical resection. The diagnosis will be confirmed by the Laboratory of Pathology, CCR, NCI. Tumor must have epithelioid histology determined by the Laboratory of Pathology at the NCI. If the patient has biphasic histology, the epithelioid component must be >50%  Have provided archival tumor tissue sample or able to provide 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 disease locally accessible disease to suitable for intratumoral injection of LMB- 100. Have measurable disease based on RECIST 1.1. Lesions in a previously irradiated area are considered measurable if progression has been demonstrated in such lesions. Subjects must have received prior immune checkpoint therapy with anti-PD-1/PD-L1 inhibitors alone or in combination with anti-CTLA4 blocking antibodies, as well as platinum based chemotherapy. Age >= 18 years. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. Evaluation of ECOG is to be performed within 28 days prior to initiation of study therapy.  Have adequate organ and marrow function as defined below:  System and Laboratory Value  Hematological<TAB>  hemoglobin >= 9 g/dL(a)  absolute neutrophil count >= 1,500/mcL  platelets >= 100,000/mcL  Hepatic  total bilirubin <= 2.5 X institutional ULN OR direct bilirubin <=ULN for participants with total bilirubin levels >1.5 X ULN  AST and ALT <= 2.5 X institutional ULN (<= 5 X ULN for participants with liver metastases)  Renal  Creatinine <=1.5 x ULN OR Measured or calculated(b) creatinine clearance (GFR can also be used in place of creatinine or CrCl) >= 50 mL/min for participant with creatinine levels; > 1.5 X institutional ULN  Coagulation  International normalized ratio (INR) OR prothrombin time (PT); Activated partial thromboplastin time (aPTT): <=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.  Criteria must be met without erythropoietin dependency and without packed red blood cell (pRBC) transfusion within last 2 weeks. Creatinine clearance (CrCl) should be calculated per institutional standard. Must have left ventricular ejection fraction >50%. The effects of LMB-100 on the developing human fetus are unknown. For this reason and because ipilimumab is a Category C agent, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) while on study therapy and for four months after the last dose of study therapy. 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. Ability of subject to understand and the willingness to sign a written informed consent document.  EXCLUSION CRITERIA:  Is currently participating in or has participated in a study of an investigational agent or has used an investigational device within 3 weeks prior to initiation of study therapy.  Note: Participants who have entered the follow-up phase of an investigational study may participate as long as it has been 3 weeks after the last dose of the previous investigational agent. Patients with active devices will be excluded from the study  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 initiation of study therapy. Has active systemic issues as bleeding diathesis or active infections Presence of a clinically significant pericardial effusion Has severe hypersensitivity (>=Grade 3) anti-CTLA4 therapies and/or any of their excipients. Has received prior radiotherapy to the site of local administration Subjects who have received LMB-100 previously Has received prior systemic anti-cancer therapy including investigational agents within 3 weeks prior to initiation of study therapy. Patients who have received prior anti-PD-1/PD- L1 or CTLA4 antibodies are eligible. Any toxicity related to these agents must have resolved to grade 1 and they must not be on systemic immunosuppressive therapies (physiologic dose of steroids are permitted). Has received prior radiotherapy to site other than target lesion within 2 weeks prior to initiation of study therapy. Participants 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 (<=2 weeks of radiotherapy) to non-CNS disease. Has not recovered from all AEs due to previous therapies to <=Grade 1 or baseline. Participants with <=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 initiation of study therapy. Has received a live vaccine within 30 days prior to initiation of study therapy. 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. Is receiving therapeutic anti-coagulation. Patients receiving prophylactic anticoagulation may be eligible if in the opinion of the study team, anti-coagulation may be stopped during the time of LMB-100 administration and tumor biopsies 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 initiation 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 QTcF interval >480 milliseconds 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 woman of childbearing potential who has a positive pregnancy test within 72 hours prior to initiation of study therapy. If the using a urine test and test 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 4 months after the last dose of trial treatment. Pregnant women are excluded from this study because LMB-100 + ipilimumab 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 + ipilimumab, breastfeeding should be discontinued if the mother is treated with LMB-100 + ipilimumab. These potential risks may also apply to other agents used in this study. 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. Positive for Hepatitis B or C (defined as Hepatitis B surface antigen reactive) or known active Hepatitis C virus (defined as HCV RNA detected) infection. or active HBV or HCV infection. 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.