For a couple of quick intros, try Learn Lua in 15 Minutes[1] and Learning Lua from JS[2]. For a bit more depth, try the Lua-users Tutorial Directory[3]. For serious depth, the two recommended by Gracana, PIL[4] and the reference manual[5], are fantastic. For an overview of the ecosystem, including some useful gamedev libraries and LÖVE-specific resources, take a look at awesome-lua[6] (my own, shameless plug).

http://tylerneylon.com/a/learn-lua/

http://phrogz.net/lua/LearningLua_FromJS.html

http://lua-users.org/wiki/TutorialDirectory

http://www.lua.org/pil/

http://www.lua.org/manual/5.1/

https://github.com/LewisJEllis/awesome-lua