Background: Pleural mesothelioma (PM) is characterised by often rapid therapeutic failure and chemotherapy resistance. While terminal resistance is well-studied, the initial transition into a drug-tolerant persister (DTP) state remains poorly understood. Methods: We established patient-derived organoids (PDOs) from malignant pleural effusions to model this transition. Cisplatin-tolerant lines were generated via repeated incremental exposure to cisplatin and compared to time-matched treatment-naive controls using RNA sequencing and Seahorse XFe96 metabolic flux analysis. Results: Integrated profiling suggested that the route to tolerance may be influenced by the underlying mutational profile. All BAP1-retained models (including those with KRAS mutations or MTAP loss) adopted a hyper-metabolic hybrid phenotype, significantly upregulating both oxidative phosphorylation and glycolysis to fuel survival mechanisms. Conversely, BAP1-deficient models entered a hypometabolic state of dormancy, characterised by global bioenergetic suppression and reduced Ki-67 proliferation. Transcriptomic analysis identified a vesicular sequestration signature (SYNGR3, VPS52, PROM2) in plastic models, suggesting non-genetic drug export as a survival strategy. Conclusions: Our findings demonstrate that mesothelioma therapeutic escape is not a uniform process. Identifying these patient-specific metabolic and transcriptomic trajectories via 3D PDOs may lead to optimised personalised therapy.