There is no difference between x32/x64 versions of LuaRT.
x64 version means that LuaRT is compiled for latest processors that have 64 bits instructions and a wide range of memory available. It needs a 64 bits version of Windows.
x32 is available for compatibility with old CPU and 32 bits Windows version, but can be run on 64 bits platform too.
If you don't know which one to use, and you have a recent computer (from the last 5 years), you should use LuaRT x64.