We had this problem a bit with Allen... I took the lid away completely and now he doesn't do that (he's cautious to remain within the confines ot the box.) BUT, he refuses to use the one in the bathroom unless nobody's home (he's a private fella ya know) and he only uses the one in the basement because people rarely go down there (only me, the laundress )

If you simply cannot remove the lid without the threat of kitty strike, then could you try fiting some sort of foam cushion between the top and bottom? It might act like a seal to keep the pee from eaking out. You can find all sorts of silicones, foam tapes etc at the home repair store.

Good luck!