Positron Emission Tomography (PET) using 18 F-FDG is recognized as the modality of choice for lymphoma, due to its high sensitivity and specificity. Its wider use for the detection of lesions, quantifica-tion of their metabolic activity and evaluation of response to treatment demands the development of accurate and reproducible quantitative image interpretation tools. An accurate tumour delineation remains a challenge in PET, due to the limitations the modality suffers from, despite being essential for quantifying reliable changes in tumour tissues. Due to the spatial and spectral properties of PET images , most methods rely on intensity-based strategies. Recent methods also propose to integrate anatomical priors to improve the seg-mentation process. However, the current routinely-used approach remains a local relative thresholding and requires important user interaction , leading to a process that is not only user-dependent but very laborious in the case of lymphomas. In this paper, we propose to rely on hierarchical image models embedding multimodality PET/CT de-scriptors for a fully automated PET lesion detection / segmenta-tion, performed via a machine learning process. More precisely, we propose to perform random forest classification within the mixed spatial-spectral space of component-trees modeling PET/CT mages. This new approach, combining the strengths of machine learning and morphological hierarchy models leads to intelligent thresholding based on high-level PET/CT knowledge. We evaluate our approach on a database of multi-centric PET/CT images of patients treated for lymphoma, delineated by an expert. Our method provides good efficiency, with the detection of 92% of all lesions, and accurate seg-mentation results with mean sensitivity and specificity of 0.73 and 0.99 respectively, without any user interaction.