If the lease had indicated in some fashion that your rental did not include this closet, that  would  be legal and enforceable. Or even if the closet being locked were at least disclosed to you prior to signing the lease, and you chose to sign it anyway, that would likely be acceptable, too. However, if you leased what you thought or should have been the entire premises, only to discover, after signing the lease, that the landlord was not giving you possession of the entire premises (i.e. he was holding this closet back), that is a breach of the lease and you could take legal action. You probably could not rescind or terminate the lease--unless having that closet is somehow critical (and it would be reasonable to the average person that it is critical)--but you may be entitled to some rent abatement or compensation for not having the space.