Accurate lesion segmentation from whole-body Positron Emission Tomography (PET)/Computed Tomography (CT) scans is essential for cancer staging and treatment planning. PET provides functional metabolic information with different radiotracers, while CT offers anatomical localization. Lesion delineation from PET/CT imaging is clinically challenging due to subtle imaging features, confounders, and inter-reader variability. Existing deep learning approaches suffer from training-related stochasticity, inconsistent predictions, missed lesions in high tumor-burden cases, and lack uncertainty quantification, limiting their clinical reliability. Using nnU-Net as a baseline, we propose an uncertainty-aware framework for whole-body PET/CT lesion segmentation that integrates (1) Bayesian ensembling to reduce training stochasticity, (2) voxel-wise uncertainty quantification with epistemic and aleatoric decomposition, and (3) epistemic uncertainty-augmented training to improve lesion detection. Two public datasets, AutoPET-III (1,611 scans) and Deep-PSMA (200 scans), comprising FDG and PSMA studies across multiple cancer types, are used for training and evaluation. Bayesian ensembling improves robustness and performance over deterministic nnU-Net models on the unseen AutoPET-III test set. Uncertainty maps highlight regions of model disagreement and correlate with misclassifications, particularly false positives. Uncertainty-augmented training improves lesion recovery at the cost of increased FPVol, reflecting a precision-recall trade-off. A case-adaptive routing strategy further improves Dice by selecting between the base and augmented models. To our knowledge, this is the first study to systematically investigate uncertainty quantification in multi-tracer, pan-cancer PET/CT segmentation and to combine Bayesian ensembling with uncertainty-aware modeling for this task.