Mesothelin-Targeted Immunotoxin LMB-100 Alone or in Combination With Nab-Paclitaxel in People With Previously Treated Metastatic and/or Locally Advanced Pancreatic Ductal Adenocarcinoma and Mesothelin Expressing Solid Tumors

Background: * Pancreatic cancer is the fourth most common cause of cancer death in the United States, claiming more than 40,000 lives each year. * Incidence nearly equals mortality with just 6% of participants living five years beyond their diagnosis. Most patients are diagnosed at an advanced stage, but even patients with early stage disease have a long term survival of less than 20%. * Mesothelin is specifically a marker of adenocarcinoma in the human disease and is not expressed in preceding pre-malignant stages of tumor development * Expression of mesothelin in pancreatic ductal adenocarcinoma (PDA) has been examined in several published studies and ranges from 86 to 100% * Recombinant immunotoxins (RITs) are antibody-based therapeutics that carry a toxin payload. RITs that target mesothelin contain a genetically engineered variant of Pseudomonas exotoxin A (PE) in which the native cell-binding domain of PE is replaced by the mesothelin-binding antibody fragment. SS1P was the first mesothelin-targeted RIT tested in patients. * LMB-100 contains a newly engineered PE fragment that has improved activity against most pancreatic cancer cell lines in vitro, and is also much less toxic than SS1P in preclinical models. The new PE contains modifications specifically designed to reduce immunogenicity of the molecule. * Pre-administration of paclitaxel with SS1P was demonstrated to increase the amount of immunotoxin internalized by tumor cells and to reduce levels of shed mesothelin in the intra-tumoral environment so that more immunotoxin could bind tumor cells. The effect is even more pronounced with NAB-paclitaxel in a pancreatic cancer model. * Initial clinical testing of LMB-100 was performed by Roche in a multi-center international first in human trial (NCT02317419). The agent was well tolerated and appeared to have decreased immunogenicity compared to SS1P based on preliminary results. * In initial and subsequent clinical testing, LMB-100 was found to have half-life of approximately 60 mins. This is shorter then that measured for previous RITs used in the clinical setting. Primary Objectives: * Arm A1 (Phase I, short infusion): --To determine the maximum tolerated dose of short infusion LMB-100 in combination nab-paclitaxel chemotherapy in participants with advanced pancreatic cancer * Arm B1(Continuous infusion single agent lead-in): --To determine the maximum tolerated dose of LMB-100 given in a continuous infusion format over 24 - 96 hours to patients with advanced solid tumors that express mesothelin * Arm B2 (Continuous infusion combination therapy) --Establish a tolerated dose of LMB-100 given by continuous infusion in combination with nab-paclitaxel chemotherapy in participants with advanced pancreatic cancer * Arm A2 (Phase II, short infusion): * To determine the objective response rate (Partial Response (PR)+Complete Response (CR) according to Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 criteria of short infusion LMB-100 in combination with nab-paclitaxel chemotherapy in participants with advanced pancreatic cancer Eligibility: * Age greater than or equal to18 years * Histologically confirmed recurrent, metastatic and/or advanced pancreatic ductal adenocarcinoma (Except for Arm B1 \[B Single Agent Lead-in\]) * For Arm B1 (Single Agent Lead-in), ONLY: Histologically confirmed solid tumor malignancy for which no curative therapy exists with at least 25% of tumor cells expressing mesothelin as determined by National Cancer Institute (NCI) Laboratory of Pathology. Determination can be made using archival tumor tissue or fresh biopsy. * Treatment must include at least one prior chemotherapy regimen * No nab-paclitaxel or paclitaxel treatment in the last four months (Except for Arm B1 \[Single Agent Lead-in\]) * Adequate organ function * Participants with human immunodeficiency virus (HIV), active hepatitis B virus (HBV) or hepatitis C virus (HCV) infections are eligible only for the Arm B1 (Single Agent Lead-in) Design: * This study is a Phase I/II open label study to assess the safety and efficacy of LMB-100 in combination with the standard of care agent nab-paclitaxel in participants metastatic and/or locally advanced pancreatic ductal adenocarcinoma * Subjects will be treated for up to 2 cycles * In Arm A1 (Phase I, short infusion) of the study, up to 3 dose levels will be evaluated. LMB-100 will be administered on days 1, 3 and 5 of a 21 day cycle and nab-paclitaxel will be administered on days 1 and 8 * Arm A2 (Phase II, short infusion), up to 20 evaluable participants (including those treated at the short infusion maximum tolerated dose (MTD) in the phase I study) will be enrolled. * Arm B1 (Continuous infusion single Agent Lead-in), escalating doses of single agent LMB-100 will be administered. The study drug will be given as a continuous infusion for the 1, 2, 3, or 4 days of a 21-day cycle. * Arm B2 (Continuous infusion, combination therapy) will be initiated after completion of both Arm A1 and Arm B1 Single Agent Lead-in. It will test a single dose level of LMB-100 based on data from the Lead-in given in combination with nab-paclitaxel. LMB-100 will be given as a continuous infusion for the 1, 2, 3 or 4 days of a 21-day cycle. Nabpaclitaxel will be given on Day 1 and Day 8. * The Arm A2 (Phase II, short infusion) portion of the study will be conducted in a Simon Minimax two stage phase II design. The first stage will enroll 13 evaluable participants, including the six participants treated at the short infusion MTD from phase I. If 1 or more has a response, then accrual would continue until a total of 20 evaluable participants have been enrolled.