Landlord threatening to evict...is this legal?

The application means nothing in court. Review your lease as to what, if anything, it says about pets. Even if nothing is mention (which would mean no fee), your landlord can still require you to remove the dog if it becomes a nuisance. Also, something to keep in mind for future leases, five hundred dollars isn't uncommon when it comes to pet fees. It's pretty uncommon to not to have to pay them.