and a door is a door. there is no functional difference in the rules between a door on a bay holding mechbays, and a door on one holding fighter bays. what makes a bay door a fighter door is the fighter bays inside, and what makes one a mech door is being to a bay with mechbays inside.
since LAM's can use either a fighter or mech bay, depending on mode, it can thus use either type of door as well. you don't need extra doors for LAM's. or to leave bays empty.
(i think some of the confusion is the fact that we refer to compartments on a dropship or warship as "bays" but we also refer to the storage and repair cubicals for fighters, mechs,and vehicles as "bays" as well when you will usually see several such cubicals in each dropship compartment.)
If i was loading a Leopard i could fit 6 LAMs aboard.. 4 in the mech cubicals in mech mode and 2 in the fighter cubicals in fighter mode. i could launch all 6 using the 6 doors on the dropship.. 2 of which go to the bay with the fighter cubicles, 4 to the bay with the mech cubicals.
they'd launch in these modes but could immediately change modes to whatever they need.. the mech mode LAm's shifting to fighter mode in space or the fighter mode LAM's shifting to mech mode on a planet, etc.
likewise when they return to the dropship they'd board in much the same way.. 4 of them shifting to mech mode to go to the mech cubicals and 2 into fighter mode to land in the fighter cubicals.