If you look at the LXC homepage, you'll notice
liblxc referred to, implying there's an ABI, and if you look further down, you'll notice a link to the C API documentation.
That page looks empty at first because it has been done (rather lazily, I think) with doxygen. However, if you start clicking around you'll find stuff. Just keep in mind, again, that it's auto-generated from source and perhaps not a huge effort was put into annotating that in a doxygen friendly way. Another perhaps confusing thing is all the actual functions are documented via function pointers in data structures (looks like an OO-ish interface).
But if you already know how to use LXC on the command line you should be able to deduce some correlations.