I've been maintaining an open source LaTeX web API called the CLSI (https://github.com/scribtex/clsi) for a few years now. This powers ShareLaTeX and ScribTeX, and I'm really keen for others to use it, and for the standard to evolve with more focus than just what I decide to add on a whim! As far as I'm aware, it's the only documented API for calling an online LaTeX compiler, and the design of the API is meant to be separate from the backend, so that the other online services could also expose a compatible API. If you're interested in perusing some sort of integration for LyX, then we need to talk further! My email address is in my profile.