If so, would we have the right to evict him from the premises?
Real Estate Attorney
This is a question of New Jersey law, about which I make no claims of knowledge.
Speaking generally, you would have a right to evict him under two circumstances. First, you could evict him if the lease stated that any misrepresentation on the application would be a breach of the lease. Second, you could evict him if the misrepresentation somehow caused you damage.
Consult New Jersey counsel.