It all depends on your county's rules. It would be best to talk to your superintendent. Our county's superintendent was at one time also big into showing rabbits (she is a judge, etc) so she changed all the rules and was super strict about it must be purebred and followed all ARBA rules. It does not have to be registered or have a pedigree, but it must be a purebred, no dq's, must have a proper tatoo, no signs of sickness or it was not allowed in, period. I personally see no reason why there couldn't be a pet class, but would need to get that changed in our rule book.
So, because lionheads are not recognized yet, it would not be allowed at our fair. We have had rabbits dq'd because they had a broken tail, the judge found it when examing it, just a small kink. It was in a meat pen and said it was too bad, they pen would have won Grand Champion meat pen, instead it was dq'd. That was dumb if you asked me, as they are being judged on meat, what does a broken tail have to do with that? By the way, it was an old injury and they are not uncommon, can happen easily in the next box, rough housing with litter mates, get caught in the cage, etc. Anyway, not all 4-H rules are the same, that was my point.
So, because lionheads are not recognized yet, it would not be allowed at our fair. We have had rabbits dq'd because they had a broken tail, the judge found it when examing it, just a small kink. It was in a meat pen and said it was too bad, they pen would have won Grand Champion meat pen, instead it was dq'd. That was dumb if you asked me, as they are being judged on meat, what does a broken tail have to do with that? By the way, it was an old injury and they are not uncommon, can happen easily in the next box, rough housing with litter mates, get caught in the cage, etc. Anyway, not all 4-H rules are the same, that was my point.