Can a dog have 20 puppies in a lifetime?

YES - although it can change depending on the dog you have.

large breeds - most large breeds have between 5-13 puppies each litter and each dog have around 5 litters in their lifetime (although it is not recommended to breed dogs so often) so yes it is deffinately possible.

smaller dogs however have few puppies and it might therefore be unlikely for small dogs to have up to 20 puppies in a lifetime although it is not impossible.