Hmm, well, such webserver exists: ldraw.org ;-),
however, it probably would be more practical to keep a .zip with the latest parts update on YOUR server,
to avoid all the traffic to ldraw.org.
I really would suggest to implement parsing etc. in JavaScript, full on client side,
it is very easy to do, and as long as you have a .zip available with the latest parts update,
you can display any model a user likes.
You can download the .zip do the browser cache of the client.
And put an input control onto a page, so a user can browse for a model (*.ldr or *.mpd file)
to display OR specify the URL to it.
Then you would parse it by JavaScript, use the .zip library I just mentioned, and - voila - send it to WebGL.