in reply to
LWP::UserAgent vs. NTLM Challenge/Response
I believe the stuff that LWP does deals with HTTP headers, and in your case it looks like the info is in form fields. You're not likely to find a pre-made solution that fits this method. You could possibly roll your own with Authen::NTLM. The first step would probably be to log into the site using your browser and watch how it works using something like Paros or Charles.
Speaking of those tools, an alternative might be to watch if they set a cookie, like vcTheGuru suggested. If so, then you might be able to hardcode a spoofed cookie to trick the site into thinking you have one long never-ending session.
Even if neither of my ideas work out, I'd suggest trying one of the tools I linked to above. They'll help take the guesswork out of what you need to do.