i would drill it on the lathe, and if possible use a colt drill bit, although I dont have one that big, and for a one off hole it would be expensive (if they even make one). I would also start it with a centre drill bit, or the point of a skew.
I am not sure whether other people use a dab of water or oil on the drill bit to help cool it- I do on ebonite, but am less regimented with doing so on acrylic.