I would like to know how could you automate that part from within a script (using LWP or Mechanize)?

What have you tried and had fail? If I remember correctly there are examples of how to do that in the {cpan://LWP::UserAgent] documents. Also if you do a Super Search there exist several examples that have been posted here in PM, including one to batch download the entire set of JPEG files that were published by Sports Illustrated for their swimsuit edition.