In metastatic breast cancer, bone metastases are prevalent and associated with multiple complications. Assessing their response to treatment is therefore crucial. Most deep learning methods segment or detect lesions on a single acquisition while only a few focus on longitudinal studies. In this work, 45 patients with baseline (BL) and follow-up (FU) images recruited in the context of the EPICUREseinmeta study were analyzed. The aim was to determine if a network trained for a particular timepoint can generalize well to another one, and to explore different improvement strategies. Four networks based on the same 3D U-Net framework to segment bone lesions on BL and FU images were trained with different strategies and compared. These four networks were trained 1) only with BL images 2) only with FU images 3) with both BL and FU images 4) only with FU images but with BL images and bone lesion segmentations registered as input channels. With the obtained segmentations, we computed the PET Bone Index (PBI) which assesses the bone metastases burden of patients and we analyzed its potential for treatment response evaluation. Dice scores of 0.53, 0.55, 0.59 and 0.62 were respectively obtained on FU acquisitions. The under-performance of the first and third networks may be explained by the lower SUV uptake due to treatment response in FU images compared to BL images. The fourth network gives better results than the second network showing that the addition of BL PET images and bone lesion segmentations as prior knowledge has its importance. With an AUC of 0.86, the difference of PBI between two acquisitions could be used to assess treatment response. Clinical relevance- To assess the response to treatment of bone metastases, it is crucial to detect and segment them on several acquisitions from a same patient. We proposed a completely automatic method to detect and segment these metastases on longitudinal 18F-FDG PET/CT images in the context of metastatic breast cancer. We also proposed an automatic PBI to quantitatively assess the evolution of the bone metastases burden of patient and to automatically evaluate their response to treatment.