...

my $url = "http://www.letssingit.com/frame_menu.html";

my $query = ...;

...

$mech->submit_form(
   form_name => 'search', 
   fields    => {
      s => $query,
      l => 'song',  # or 'artist' or 'album' or 'lyrics'.

      # The only button doesn't have a name, so no
      # need to put anything here for the button.
   },
);

...