Terminating a lease usually requires that all payments owed, AND the residual amount be paid, plus any contractual termination fee or end of lease purchase fees. You will 99 % NEVER get enough on a trade in to cover all the charges, more so if you are early in the lease where depreciation is highest.
Few options ...
Call the leasing company, and TALK. See what they say. Given it is a health issue, there might be something they can do. Never hurts to ask.
Try and find someone to assume the lease. There are various sites online dedicated to breaking a lease. And, if there was a downpayment involved, the lease payments are often lower, and more attractive to somebody looking to assume the lease. The person looking to assume the lease would need to qualify with the leasing company, and there is usually a transfer fee involved as well.
Try and sell the car privately. You will get more for it, and MAYBE even get close to the lease payout amount, depending on brand, age, condition etc.
Or stop paying, let the car get re-possessed, and deal with any credit issues / recovery actions at a later date. That might take years ...