This study addresses critical gaps in automated lymphoma segmentation from PET/CT images, focusing on issues often overlooked in existing literature. While deep learning has been applied for lymphoma lesion segmentation, few studies incorporate out-of-distribution testing, raising concerns about model generalizability across diverse imaging conditions and patient populations. We highlight the need to compare model performance with expert human annotators, including intra- and inter-observer variability, to understand task difficulty better. Most approaches focus on overall segmentation accuracy but overlook lesion-specific measures important for precise lesion detection and disease quantification. To address these gaps, we propose a clinically relevant framework for evaluating deep segmentation networks. Using this lesion measure-specific evaluation, we assess the performance of four deep networks (ResUNet, SegResNet, DynUNet, and SwinUNETR) across 611 cases from multi-institutional datasets, covering various lymphoma subtypes and lesion characteristics. Beyond standard metrics like the Dice similarity coefficient, we evaluate clinical lesion measures and their prediction errors. We also introduce detection criteria for lesion localization and propose a new detection Criterion 3 based on metabolic characteristics. We show that networks perform better on large, intense lesions with higher metabolic activity. Finally, we compare network performance to physicians via intra- and inter-observer variability analyses, demonstrating that network errors closely resemble those made by experts, i.e., the small and faint lesions remain challenging for both humans and networks. This study aims to improve automated lesion segmentation's clinical relevance, supporting better treatment decisions for lymphoma patients. The code is available at: https://github.com/microsoft/lymphoma-segmentation-dnn.