We have a lobby in the entrance area---after the foyer---we are thinking of removing 1 drywall of that area to open up the lobby---which will remove the powder room and closet---but the concern is will that affect the structure or support to the top floor.

There are bearing walls and there are partitions.
You can tell a lot by measuring the thickness of the walls. Bearing walls are usually an inch thicker than non bearing partition walls.
You can tell a lot by finding a center wall down the middle of the length of the house (long way) even if it has doorways and breaks in the length. Often side walls can come down, but not always, depending on the span of the joists they are under. They run parallel to joists.
Aside from that, there are too many questions to ask about the design of the house.
There's a saying 'Every wall is a bearing wall and no wall is a bearing wall.'
That means that every partition helps keep the house from racking/swaying and every bearing wall can be taken down, if a big enough beam is put in it's place.
I suspect that your closet and powder room can be removed, but don't quote me on it.