What is the ruling on living in an apartment with a lifetime lease or a long-term lease (150-200 years), with a clause for an annual percentage or fixed amount increase, knowing that no other housing is available?

For the validity of a rental contract (ijarah), the duration must be known. It is not valid if the duration is unknown, such as "for life" or for a period not typically lived out. It is permissible to increase the rent annually by a specific amount or a known percentage, such as saying: "Your rent this year is such-and-such, and the second year is such-and-such." However, it is not valid to say: "And the second year is 'according to its account'," because the rent would then be unknown.