On a Lease Purchase (LP) an amount of the total cost of the vehicle will be deferred (estimated future resale value/ residual value) until the end of the agreement. Your monthly payments will be based on the total cost less the deferred amount. The deferred payment must be paid at the end of the agreement to own the vehicle.
On a LP agreement the deferred element (residual value/final payment) is estimated based on the vehicle usage, meaning the vehicle could be worth less than the lenders estimation which could result in negative equity.
The difference between a Lease Purchase and a Personal Contract Purchase PCP is that the deferred payment on a Lease Purchase is an estimate of how much the car maybe worth, where as on a PCP the Guaranteed Minimum Future value (GMFV) is the minimum the car will be worth and there is no option to return the car.