I'm having major lag issues with games on the larger maps - are there any settings I can change, or anything like that, that might help reduce the lag a bit? It makes it really difficult to manage the map at all on mobile.
That is largely dependent on your phones capabilities. The larger maps are much more of a strain on some phones processors due to so much going on. I would suggest trying to clear the phones cache, and more so, would suggest playing on PC to help ensure better function.