Accurate detection and segmentation of diffuse large B-cell lymphoma (DLBCL) from PET images has important implications for estimation of total metabolic tumor volume, radiomics analysis, surgical intervention and radiotherapy. Manual segmentation of tumors in whole-body PET images is time-consuming, labor-intensive and operator-dependent. In this work, we develop and validate a fast and efficient three-step cascaded deep learning model for automated detection and segmentation of DLBCL tumors from PET images. As compared to a single end-to-end network for segmentation of tumors in whole-body PET images, our three-step model is more effective (improves 3D Dice score from 58.9% to 78.1%) since each of its specialized modules, namely the slice classifier, the tumor detector and the tumor segmentor, can be trained independently to a high degree of skill to carry out a specific task, rather than a single network with suboptimal performance on overall segmentation.