Tertiary lymphoid structures (TLS) are organized clusters of immune cells, whose maturity and area can be quantified in whole slide image (WSI) for various prognostic tasks. Existing methods for assessing these characteristics typically rely on cell proxy tasks and require additional post-processing steps. In this work, We focus on a novel task-TLS Semantic Segmentation (TLS-SS)-which segments both the regions and maturation stages of TLS in WSI in an end-to-end manner. Due to the extensive scale of WSI and patch-based segmentation strategies, TLS-SS necessitates integrating from neighboring patches to guide target patch (target) segmentation. Previous techniques often employ on multi-resolution approaches, constraining the capacity to leverage the broader neighboring context while tend to preserve coarse-grained information. To address this, we propose a GNN-based Neighboring Context Aggregation Framework (GNCAF), which progressively aggregates multi-hop neighboring context from the target and employs a self-attention mechanism to guide the segmentation of the target. GNCAF can be integrated with various segmentation models to enhance their ability to perceive contextual information outside of the patch. We build two TLS-SS datasets, called TCGA-COAD and INHOUSE-PAAD, and make the former (comprising 225 WSIs and 5041 TLSs) publicly available. Experiments on these datasets demonstrate the superiority of GNCAF, achieving a maximum of 22.08% and 26.57% improvement in mF1 and mIoU, respectively. Additionally, we also validate the task scalability of GNCAF on segmentation of lymph node metastases.