yup -- search through the $mech->forms array (elements are HTML::Form objects) for the one you want (yes could be slightly more efficient w/a loop instead of grep).

my @forms = $mech->forms;
my ($form_number) = grep { $forms[$_-1]->action eq 'http://www.lyricsd
+ownload.com' } 1 .. @forms;
$mech->submit_form(
  form_number => $form_number,
  fields => {
    ...
  },
);
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