Stadium bosses, the London Legacy Development Corporation, have spent about £17,000 fighting a ruling that the contract should be made public.
It argues the deal contains commercially sensitive information.
Last month the London Assembly called for the rental agreement to be published in full.
Monday's independent tribunal hearing is open to the public, although it is likely to be several weeks before a decision is announced.
West Ham are in their final season at the Boleyn Ground before moving about three miles to the former Olympic Stadium in east London.