Not at all. You can start with whichever one you want. While they do occur in the same universe, each case is self-contained and standalone. Chronologically, Lights, Camera, Murder! takes places before Death in La-La Land but you do not need to have solved the former to start on the latter.
Do I need to complete the cases in a specific order?

Written by Vaughn I.
Updated over a week ago
Updated over a week ago