I'm just answering to give you some insights on how the SDL is used. As you said before it's not a game engine (it's just a library actually). Furthermore, it is not object oriented at all and you don't have some easy animation facilities (you have to code them by yourself).
How it works (I used the C version but I guess the Lua binding should be similar):
Include the headers needed to build the project on the platform you want.
Design your own game loop in which you will set up (at least) a whole event processing system, frame rate manager and a "screen cleaner (or updater)" (I'm insisting on the fact that you have to manually refresh your screen using the SDL_flip_screen routine which is something that is not one of your concerns at all with Corona).
Then, code your game using all the "mechanics" you made before.
The SDL is a low level library (don't expect to have an easy to use GUI framework or the storyboard framework of Corona for instance).
Finally, this library was used to port Civilization III to Linux, so yes it works but it will ask you a lot of energy to have something like you had with Corona ;)
PS: I am not a native English speaker, so please let me know if I wasn't clear :)