The one time I scripted something similar to this, I prompted interactively for the LJ password and had the script do its own login. The resulting cookie worked with LWP for my own purposes (exporting locked posts from my own journal). However, that was around 2004 or so and LJ has probably changed quite a bit since then.

Perhaps they have done something that specifically blocks the LWP user agent. If that's the case, you could see if changing the user agent string helps. Good luck!