A robot deployed in a home over long stretches of time faces a true lifelong learning problem. As it seeks to provide assistance to its users, the robot should leverage any accumulated experience to improve its own knowledge and proficiency. We formalize this setting with a novel formulation of lifelong learning for task and motion planning (TAMP), which endows our learner with the compositionality of TAMP systems. Exploiting the modularity of TAMP, we develop a mixture of generative models that produces candidate continuous parameters for a planner. Whereas most existing lifelong learning approaches determine a priori how data is shared across various models, our approach learns shared and non-shared models and determines which to use online during planning based on auxiliary tasks that serve as a proxy for each model's understanding of a state. Our method exhibits substantial improvements (over time and compared to baselines) in planning success on 2D and BEHAVIOR domains.