Suppose the PCs are up against a pair of dragons. Both dragons have lair actions per the MM. Would you allow both dragons to use a lair action at the same time or would you limit it to one or the other but not both? How about generally?
I'd say each dragon can use a Lair Action, but in some cases using the same Lair Action again causes a previous effect to end e.g. the green dragon's wall of tangled brush.
Both get their Lair actions and Legendary Actions if they have those. If the PCs are facing 2 Dragons, they need to feel the full brunt of that choice. Running is always an option that should be allowed.
So, extend this to a situation with 10+ critters where, per the MM, each has lair actions. Do you still let each critter have those lair actions? Or restrict it to just the boss critter(s)?