Am I, or the person to whom I offered the food, obligated to return a dish belonging to the rented apartment I left, or to compensate for its price?

It is permissible for the tenant to lend out what he has rented from an object, as the apartment and its contents are a trust in his hand, and he is not liable for their damage except through his negligence or transgression. If the tenant is negligent in following up on the lent object and it is not returned, he is liable for it to its owners, either by returning it, or purchasing a replacement for it, or paying its value.