The page you linked refers to Lua 5.0. This has changed since. The variable inside Lua that controls the package path is now called package.path and the environment variable is still called LUA_PATH. For the .so modules, the variables are package.cpath and LUA_CPATH.
Since Lua 5.2, there are also versioned variants of the environment variables: LUA_PATH_5_2, LUA_CPATH_5_2, LUA_PATH_5_3, LUA_CPATH_5_3. These take precedence over the unversioned ones when available.
-- Hisham