No, unfortunately. The exact details would be extremely complex and would probably require a diagram, heh, but a) OpenID isn't a trustworthy form of authentication for something like this, and b) using OpenID in that fashion, even if it were reliable "enough", would require code changes on LJ's part, which I sincerely doubt they'd be willing to make.

There is a protocol that would do the trick properly -- OAuth -- that many services support, and we are working on an implementation of it, but that will only work with sites that use OAuth (such as Twitter, and a bunch of others I can't remember right now off the top of my head) -- LJ does not support OAuth.