Normalized macro names to all start with AX_LUA_CHECK_.
Changed the file name to ax_lua_check.m4.
Changed LUA_INCLUDES to LUA_INCLUDE and LUA_LIBS to LUA_LIB, so to match ax_lua.m4.
Fixed inverted AC_MSG_RESULT.
Updated documentation, moved all documentation to the top of the file.
Improved tests.
Added .gitignore for tests.