"Want to make use of already authenticated session that I started on mozilla."

Is there a specific reason for this? If not, try the credentials() method?

use LWP::UserAgent qw();
my $ua = LWP::UserAgent->new;
my $netloc = 'http://www.buddhism-dict.net/cgi-bin/xpr-dealt.pl:80';
$ua->credentials(
   $netloc,
   'CJK-E and Buddhist Dictionaries', # basic realm
   'guest',  # user
   '',       # empty pw
);
my $response = $ua->get($netloc);
[download]

Example taken from Rosetta Code.