"Depth" is like eight or nine deep and only 13 players can be on the active roster a night. It wouldn't be that difficult to find decent minimum contract role players after using the mid-level exception.
Given that most playoff rotations shorten to 8 players, that means the Lakers, after signing 1 max player and 1 MLE player, would need 3 extra players worthy of playoff minutes that would also agree to sign for league minimum contracts.
Oh and good luck not getting injured.
There's a reason most championship contending teams have an end of the bench rotation held together by duct tape and elbow grease. The Lakers have a real possibility of not even having a good 6th man.