If you set the default protection level on your LiveJournal to friends-lock, it will pick the default for the site, rather than the post.
(I do that with mine: the DW defaults public, LJ defaults friends-locked)
However, note that if you edit the access level on the DW side once it's posted, the LJ side will pick it up. (I just tested with a post that's locked here: edit it to public here, LJ edits to public too. Protect it, LJ picks up the protection again.) It won't do this for content edits, though, just things that touch the access level.
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(I do that with mine: the DW defaults public, LJ defaults friends-locked)
However, note that if you edit the access level on the DW side once it's posted, the LJ side will pick it up. (I just tested with a post that's locked here: edit it to public here, LJ edits to public too. Protect it, LJ picks up the protection again.) It won't do this for content edits, though, just things that touch the access level.