In Evolutionary Robotics, Lexicase selection has proven effective when a single task is broken down into many individual parameterizations. Evolved individuals have generalized across unique configurations of an overarching task. Here, we investigate the ability of Lexicase selection to generalize across multiple tasks, with each task again broken down into many instances. There are three objectives: to determine the feasibility of introducing additional tasks to the existing platform; to investigate any consequential effects of introducing these additional tasks during evolutionary adaptation; and to explore whether the schedule of presentation of the additional tasks over evolutionary time affects the final outcome. To address these aims we use a quadruped animat controlled by a feed-forward neural network with joint-angle, bearing-to-target, and spontaneous sinusoidal inputs. Weights in this network are trained using evolution with Lexicase-based parent selection. Simultaneous adaptation in a wall crossing task (labelled wall-cross) is explored when one of two different alternative tasks is also present: turn-and-seek or cargo-carry. Each task is parameterized into 100 distinct variants, and these variants are used as environments for evaluation and selection with Lexicase. We use performance in a single-task wall-cross environment as a baseline against which to examine the multi-task configurations. In addition, the objective sampling strategy (the manner in which tasks are presented over evolutionary time) is varied, and so data for treatments implementing uniform sampling, even sampling, or degrees of generational sampling are also presented. The Lexicase mechanism successfully integrates evolution of both turn-and-seek and cargo-carry with wall-cross, though there is a performance penalty compared to single task evolution. The size of the penalty depends on the similarity of the tasks. Complementary tasks (wallcross/turn-and-seek) show better performance than antagonistic tasks (wall-cross/cargo-carry). In complementary tasks performance is not affected by the sampling strategy. Where tasks are antagonistic, uniform and even sampling strategies yield significantly better performance than generational sampling. In all cases the generational sampling requires more evaluations and consequently more computational resources. The results indicate that Lexicase is a viable mechanism for multitask evolution of animat neurocontrollers, though the degree of interference between tasks is a key consideration. The results also support the conclusion that the naive, uniform random sampling strategy is the best choice when considering final task performance, simplicity of implementation, and computational efficiency.