The question's worded somewhat confusingly. H disapproves and wants out of what? The lease, the partnership (if there is one), both?
I don't see a breach of duty of loyalty (unless, perhaps, if G was not candid and did not disclose to H that he signed a new lease for the partnership). It looks like you've got a simple partnership formed by implication here (go through the elements: manifestation of intent, mutual control, some form of contribution by either party, profit sharing). If that's the case, either partner can unilaterally withdraw (barring an express partnership agreement to the contrary). Even if there's an express partnership agreement preventing unilateral withdrawal, H can still withdraw, it's just that this will amount to wrongful dissolution and G will then be allowed to continue the partnership in H's absence (which would otherwise require G's consent) upon paying H the value of his partnership interest, minus goodwill, minus any damages caused by H's wrongful dissolution.
Plus, you've got G committing the partnership to a lease. Is H bound by G's commitment to the lease? Partners are both agents and principles for one another. Under the RUPA, any partner can bind the partnership. And under RUPA, H would be liable on the lease to the extent that the partnership could not satisfy the obligation.
Those are a few things to think about, and I'm sure I'm missing quite a few more (having had Bus. Org. some time ago).