It can. Lightmap is not recalculated every frame. So if you have shadow being cast on the door, that shadow will move with the door 
(or rather, piece of the shadow that is on the door)
It’s a compromise. If you want your scene to look consistent before you disrupt it (open the door, call lift, call platform, etc.), you opt in for Quake 3-like static lighting approach, where it all looks good until you start interacting with doors/plats/etc.
Another way (and that can’t be done in Quake 3, but in FOSS engine that support Quake 3 maps) is to bake ambient and GI, but use real-time shadows. This way even when doors/etc. move, lighting on them still pretty much looks like static geometry and since shadows are all dynamic, you don’t even notice the difference in ambient/GI lighting.