The LPG BBQ on our back deck has a lid, and our setup is very common. (Keep in mind when we say “BBQ” we usually mean grilling, which is not what many Americans would call “BBQ”.)
If you go to Bunnings and look for a BBQ, heaps of them have lids.
Almost all of the barbecues you can buy now at Bunnings or Barbecues Galore (probably the two biggest Australian retailers for barbecues by far), have lids/hoods.