A full game or application is not needed; just a core library that ideally can:
The platform is a closed system that can only run Lua, so I don't even have access to run a C++ engine via Lua bindings. I would need to translate the C++ to Lua, which I'd ideally like to avoid but am not opposed to if there's no other way (unless it's a boatload of code).
Lua (v.5.1) chess engine is here.
I suggest you create a lua binding that allows you to use UCI. Then you can use multiple engines.
I do not know of any pre-exisiting chess library bindings.... though I could be wrong
If you are interested in writing a chess engine you might want to have a look at the Computer Chess Blog. It documents the creation of a chess engine from the start including full C# code listings.