Is it permissible to purchase a car in installments from the dealership through a lease-to-own system, and does this system fall under usury, especially if the buyer is unable to purchase directly and needs an intermediary?

There is no harm in a person seeking the help of a relative to carry out a transaction, then selling or leasing the car to them. As for ruling on the transaction itself, whether it is a sale or a lease-to-own, it depends on knowing its details and conditions, as companies and banks differ in their methods of dealing. As for necessity, which permits the forbidden, scholars have defined it as a person reaching a point where they would perish or be close to perishing if they do not consume the forbidden item. It has controls, including: that it must be present, not anticipated; that there is no other way to avert it; and that its measure must be observed.