Out of curiosity I tried to simply replace FGU's lua5.1.dll with a compiled LuaJIT dll. This is said to work with Civilization, so it they could have been compatible with each other. Unfortunately FGU then claims to not being able to find said dll, so no dice.
No idea if some kind of version check is involved or if FGU's Lua dll is differently structured?! But it was worth a try.