I gave the button an on click event handler and made it create a new window with a label in it above the original window. It all seems to be working pretty well.
Next I think I need to create some more components to allow me to build the game window from.
Edit: Part of the problem that I'm hitting is that Lua doesn't really have a concept of classes and so has no concept of "constructors". A lot of the things that I am doing would be a ton easier if I could write constructors. I am also having to fake out "virtual" functions to make some of the event handling for windows work properly.