How could I alter a mens polo shirt to be Lolita?

Very carefully. It would have to be a cutsew for Casual Lolita though because the fabric wouldn’t work at all for a blouse. Something like this wouldn’t be too hard to do with it since you wouldn’t have to worry about messing with the collar. This would work as well if you have the extra materials to put into it. Your biggest issue would probably be to get the nice fitted shape a cutsew should have out of a mens shirt. I honestly think you would be better off using a nice t-shirt to make alterations though because the usual Polo fabric is just weird.