Generalized behavior is a long standing goal for evolutionary robotics. Behaviors for a given task should be robust to perturbation and capable of operating across a variety of environments. We have previously shown that Lexicase selection evolves high-performing individuals in a semi-generalized wall crossing task–i.e., where the task is broadly the same, but there is variation between individual instances. Further work has identified effective parameter values for Lexicase selection in this domain but other factors affecting and explaining performance remain to be identified. In this paper, we expand our prior investigations, examining populations over evolutionary time exploring other factors that might lead to generalized behavior. Results show that genomic clusters do not correspond to performance, indicating that clusters of specialists do not form within the population. While early individuals gain a foothold in the selection process by specializing on a few wall heights, successful populations are ultimately pressured towards generalized behavior. Finally, we find that this transition from specialists to generalists also leads to an increase in tiebreaks, a mechanism in Lexicase, during selection providing a metric to assess the performance of individual replicates.