--- a/cmake_modules/FindLUA.cmake
+++ b/cmake_modules/FindLUA.cmake
@@ -36,7 +36,7 @@
   ${_LUA_FIND_VERSION_SHORT}
   -${_LUA_FIND_VERSION_SHORT}
 )
-SET(_LUA_NAMES luajit lua)
+SET(_LUA_NAMES ${LUA_IMPL})
 
 FIND_PACKAGE(PkgConfig)