End-to-end paradigms have demonstrated great potential for autonomous driving. Additionally, most existing methods are built upon Transformer architectures. However, transformers incur a quadratic attention cost, limiting their ability to model long spatial and temporal sequences-particularly on resource-constrained edge platforms. As autonomous driving inherently demands efficient temporal modeling, this challenge severely limits their deployment and real-time performance. Recently, linear attention mechanisms have gained increasing attention due to their superior spatiotemporal complexity. However, existing linear attention architectures are limited to self-attention, lacking support for cross-modal and cross-temporal interactions-both crucial for autonomous driving. In this work, we propose LADY, the first fully linear attention-based generative model for end-to-end autonomous driving. LADY enables fusion of long-range temporal context at inference with constant computational and memory costs, regardless of the history length of camera and LiDAR features. Additionally, we introduce a lightweight linear cross-attention mechanism that enables effective cross-modal information exchange. Experiments on the NAVSIM and Bench2Drive benchmarks demonstrate that LADY achieves state-of-the-art performance with constant-time and memory complexity, offering improved planning performance and significantly reduced computational cost. Additionally, the model has been deployed and validated on edge devices, demonstrating its practicality in resource-limited scenarios.