LWP supports SSL quite nicely, actually... so long as you have OpenSSL installed on your computer. The encryption/decryption/authentication schemes inherent in SSL are best encapsulated in a binary, which LWP can then leverage with the assistance of (I believe) the Net::SSLeay module.
Once all the pieces are in place fetching a document via SSL using LWP is as simple as get 'https://www.somethingsecure.com';
Gary Blackburn
Trained Killer