PDDLStream solvers have recently emerged as viable solutions for Task and Motion Planning (TAMP) problems, extending PDDL to problems with continuous action spaces. Prior work has shown how PDDLStream problems can be reduced to a sequence of PDDL planning problems, which can then be solved using off-the-shelf planners. However, this approach can suffer from long runtimes. In this paper we propose LAZY, a solver for PDDLStream problems that maintains a single integrated search over action skeletons, which gets progressively more geometrically informed, as samples of possible motions are lazily drawn during motion planning. We explore how learned models of goal-directed policies and current motion sampling data can be incorporated in LAZY to adaptively guide the task planner. We show that this leads to significant speed-ups in the search for a feasible solution evaluated over unseen test environments of varying numbers of objects, goals, and initial conditions. We evaluate our TAMP approach by comparing to existing solvers for PDDLStream problems on a range of simulated 7DoF rearrangement/manipulation problems.