Was there any sort of conflict between Laverne and Shirley prior to Shirley's departure?

Yes, there was some conflict between Laverne and Shirley prior to Shirley's departure. Laverne and Shirley were best friends, but they often had disagreements and arguments over various issues. For example, in the episode "The Apartment", Shirley was not happy when Laverne sublet their apartment without consulting her. In another episode, "Laverne and Shirley in the Army", Shirley was unhappy when Laverne signed them both up for the Army without her permission. In "Romeo and Laverne", Shirley was upset when Laverne started dating their neighbor, Romeo. Despite their disagreements, the two managed to remain close friends. In the end, Shirley's departure from the show was due to a contract dispute, not because of any particular conflict between the two.