I was just curious about the reason why the landlord will not allow pets. In these circumstances, it is likely that the landlord never owned pets and are very cautious about damage, pet accidents, and shedding which unfortunately many dogs and cats have that kind of reputation.
I have a dog, and eventhough she is house trained and non destructive, but she does shed a bit, so if I had to rent a place I would gladly offer a deposit and also offer to pay for a professional deep cleaning of the rental when I move. It's just a courtesy that will give the landlord some confidence in renting the place to you. You definitely don't want to ruin your relationship with your landlord by lying about not having a pet -- having them discover this would not be good.
Evicting a tenant for any reason tends to be a very difficult and lengthy proposition to the landlord, so eventhough a tenant can evicted due to a destructive or misbehaving pet it's something that most landlords wouldn't want to deal with.