Enabling lifelong learning in robots requires models that can continuously adapt to evolving tasks, environments, and user preferences while operating under strict computational and privacy constraints. We propose a framework for robot lifelong learning with composable diffusion models on edge devices where complex robot behaviors are represented as compositions of lightweight diffusion modules trained incrementally over time. Each module captures a reusable skill, preference, or environmental dynamic, and compositions are formed through learned conditioning and guidance mechanisms without retraining the full system. To support on-device deployment, we introduce parameter-efficient adaptation strategies and selective memory replay that bound compute, memory, and energy usage on edge hardware. The resulting system mitigates catastrophic forgetting, enables rapid skill recombination, and preserves data locality by keeping learning and inference fully on-device.