Smart Phones
5.1.1 Google Android?
There is direct support for Lua scripting with Android; see this announcement on the Google Open Source blog.
AndroLua enables using LuaJava to integrate regular C Lua into Android projects.
Corona allows for cross-platform Android and iPhone development in Lua.
5.1.2 IPhone Support?
Apple no longer disallows interpreters on the iPhone and there is no reason why an application cannot contain Lua; the restrictions seem to be against downloading and running scripts that access the iPhone APIs. You can see an iPhone running 'Hello world!' here.
There is a relevant question answered on StackOverflow.
Mathew Burke discusses options for iOS programming in Lua in this luanova article, including Corona and Wax.
5.1.3 Java-based Phones?
Kahlua is a project to completely implement the Lua engine in Java. The target platform is the reduced runtime J2ME found in mobile phones; the main example is a little Lua interpreter which can run on your phone. Another option is luaj.
Jill (Java Implementation of Lua Language) has been recently released.