Lua binaries are hosted on sourceforge. You don't need to remove Lua for Windows. What I do on my installation of LFW is, I overwrite the lua.exe
and lua.dll
with the respective 5.2.* files from the binaries I downloaded.
PS: Sourceforge hasn't been updated with 5.2.2 release of Lua and is still at version 5.2.1. If you want to build, you'll find the similar question that greatwolf has linked to.