When then Programming Language Shootout use to include LuaJIT, it had a benchmark against Java.
If you want to see just LuaJIT vs Lua, [1] is a good comparison.
The reason why I liked the inclusion of LuaJIT in the Programming Language Shootout was that it compared LuaJIT to other language implementations not just on speed, but memory consumption and lines of code. All of which, LuaJIT typically dominated.
https://github.com/darius/superbench is not a big fancy cross-language shootout, at all, but I tried a few little programs I actually cared about. LuaJIT 'won' in the sense that of the languages I tried it had the best combo of performance and pleasant productivity, informally. I didn't try to quantify the latter.
(Also, no Java because I wouldn't seriously consider it for hacking-for-fun.)