Positron Emission Tomography/Computed Tomography (PET/CT) has become an integral diagnostic imaging modality for various oncological indications over the past two decades. A crucial initial processing step for quantitative PET/CT analysis is segmentation of tumor lesions enabling accurate feature extraction, tumor characterization, oncologic staging, and image-based therapy response assessment. However, the growing volume of examinations, the introduction of novel PET tracers, and the increasing demand for sophisticated quantitative analyses have intensified the complexity and time requirements of these procedures. In the first run of the autoPET challenge (AutoPET I at MICCAI 2022) we provided training and test data from University Hospital Tübingen (UKT) and LMU Hospital (LMU) as well as a baseline model for automated lesion segmentation on whole-body Fluorodeoxyglucose (FDG) PET/ CT data. The challenge results demonstrated the feasibility of accurate lesion segmentation. In the second edition of the AutoPET challenge (AutoPET II at MICCAI 2023) we shifted our focus towards evaluating algorithmic robustness across different environments. This involved introducing a new test set comprising samples from various sites, utilizing different tracers and presenting diverse pathologies. We also relaxed constraints on using external and additional data. The challenge results revealed a substantial decline in performance, highlighting the critical need for the development of robust algorithms. Based on the insights of the last two challenges, we propose to expand the scope of the AutoPET III challenge to the primary task of achieving multitracer multicenter generalization of automated lesion segmentation. To this end, we provide participants access to a second, large PET/CT training dataset. This dataset introduces a new tracer, Prostate-Specific Membrane Antigen (PSMA), encompassing 597 PET/CT volumes of male patients diagnosed with prostate carcinoma. The data was acquired at LMU with a significant domain shift from the UKT training data provided in AutoPET I and II. Algorithms will be tested on PSMA and FDG data from LMU and UKT, respectively. We will use a mixed model framework to rank valid submissions accounting for the effects of different tracers and different sites. In addition, we will have a second award category where participants are invited to submit our baseline model trained with their creative data pipelines. This category is motivated by the observation that in AutoPET I and II, data quality and handling in pre- and post-processing posed significant bottlenecks. Due to the rarity of PET data in the medical deep learning community, there is no standardized approach to preprocess these images (normalization, augmentations, etc.). The second award category will thus additionally promote data-centric approaches to automated PET/CT lesion segmentation.