Where a some zoos in the U.S. that you can pet and hold Lion or cheetah cubs?

No good zoo should allow you to do this. Never be fooled by the name of a place either. If it has wild animals in captivity and they are exhibited to the public it is a zoo. They can call themselves what they like, sanctuary, ecopark, wildlife park, etc., they are still a zoos.

Wild animals are too dangerous and unpredictable to allow this stupid activity. There is always the hope that one wild animals from zoos can be released back into the wild. It is much better if they are not used to human contact for a whole host of reasons. If you find any place that does this simply resist the temptation and do not go. They are not a good zoo and they should not receive your patronage.

None of the zoos, maybe a wildlife refuge where their insurance might allow it.

no good zoo is going to let you do that. cub petting is a huge problem; most cubs are taken away from their mothers to maximize the time they can legally have contact with the public, many animals are bred with no regard to health or genetic diversity so there's always a steady stream of cubs, and cubs are still developing their immune systems so contact with the public often makes them sick. i know cubs are cute, but you need to really think about their health and well being before your desire to touch them. please only visit zoos that are aza accredited as they uphold the highest standards of animal care and welfare