Graph Transformer has shown great promise in capturing the dynamics of user preferences for sequential recommendations. However, the self-attention mechanism within its structure is of quadratic complexity, posing challenges for deployment on devices with limited resources. To this end, we propose a Communal Linear Attention-enhanced Graph TransFormer for lightweight sequential recommendation, namely CoLA-Former. Specifically, we introduce a Communal Linear Attention (CoLAttention) mechanism. It utilizes low-rank yet reusable communal units to calculate the global correlations on sequential graphs. The weights from the units are also made communal across different training batches, enabling inter-batch global weighting. Moreover, we devise a low-rank approximation component. It utilizes weights distillation to reduce the scale of the trainable parameters in the Graph Transformer network. Extensive experimental results on three real-world datasets demonstrate that the proposed CoLA-Former significantly outperforms twelve state-of-the-art methods in accuracy and efficiency. The datasets and codes are available at https://github.com/ZZY-GraphMiningLab/CoLA_Former.