In order to make the entire floor shiny. It's cliche and not an effect I particularly like, but I know I'll be asked 1,000 times to add it if I haven't already, so I figured the easiest way to make the entire floor shiny is to duplicate key geometry, flip it around the y axis and give the floor 0.75 or 0.8 opacity.
This is the EXACT way I got a shiny floor up and running for an FPS tech demo and I had the EXACT same problem... you can't lightmap the floor. I considered baking the lightmap on to the texture (acceptable for a dark, brooding game) but unless you use some sort of tiled system that's going to leave you with a very low-res texture stretched over the one surface that, because it's a bowling game, people are going to spend a lot of time staring at.
The only thing I can think of, off the top of my head, is to carry the lightmap on a separate version of the geometry which is overlayed on top of the non-lightmapped "proper" geometry. The lightmap geometry has a floor of its own so will lay a shdow over the alpha'd floor that you add; the "proper" geometry has no floor of its own, allowing players so see through to the reversed "reflection"; the reflection geometry is rendered with a lightmap but no floor of its own (it would be superfluous). That's THREE versions of essentially the same geometry, but if your scene is low poly enough it *might* still be preferable to rendering another scene and applying it as a texture.