Lower extremity computed tomography (CT) contains clinically relevant information for body composition analysis, sarcopenia assessment, and musculoskeletal disease monitoring, but extracting these measurements at scale requires accurate tissue segmentation and an automated quantification workflow. Existing public segmentation tools are not designed for comprehensive lower extremity CT analysis, particularly for clinically important inter/intramuscular adipose tissue, and most public methods only provide mask prediction rather than an end-to-end quantification system. To address this problem, we present LegSegNet, a deep learning system for lower extremity CT tissue segmentation and body composition quantification. Given an input CT scan, LegSegNet segments bone, skeletal muscle, subcutaneous adipose tissue, and inter/intramuscular adipose tissue. It then computes quantitative tissue measurements for downstream analysis. We developed the segmentation model using 1,302 manually annotated CT slices and evaluated it on 900 held-out test slices, with all annotations reviewed by radiologists. We benchmark LegSegNet against a broad set of 2D segmentation methods, including CNN-based models, transformer-based models, and finetuned foundation models, and further evaluate its generalization on an external public CT dataset. LegSegNet achieves the best overall segmentation performance, with an average Dice score of 89.31 on the held-out test set. To our knowledge, LegSegNet is the first publicly available end-to-end system for lower extremity CT tissue segmentation and quantification, providing a practical evaluation tool for future computer vision research in medical image analysis. The code and model weights are available at: https://github.com/mazurowski-lab/LegSegNet