In addition to chromatic's comment, you'll also need to define the LSAspace variable that page wants. This script works for me:

#!/usr/bin/perl -w
use strict;
use HTTP::Request::Common qw(POST);
use LWP::UserAgent;

my $ua = new LWP::UserAgent;
my $req = POST 'http://lsa.colorado.edu/cgi-bin/LSA-sentence-x.html',
        [ txt1 => 'I hate Jimmy. I love Jimmy.', 
          LSAspace =>'General_Reading_up_to_1st_year_college'];
my $content = $ua->request($req)->as_string;

print $content;
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