You definitely need a redistribution of LÖVE (love2d) on your platform to run the game. LÖVE itself needs Lua. So, you need both.
As for the code, you might need git if you want to keep code history (you can "git clone" game repository), or just download a zip archive and you're good to go.
I used sublime text at the time to edit files, and will definitely recommend it, although I'm not using it anymore.