There are several possible benefits in a lease/purchase. At the same time there are potential pitfalls. The agreement must be extremely specific and outline in detail how (and if) the monthly payments will be applied. It is typical, that a certain percentage or dollar amount of the monthly rent is applied towards the down payment or purchase price- It is not mandatory, but typical.
Usuallly, the selling price is predetermined at the time the lease starts. There are many different ways to go about the process. Lease/Option, Lease Purchase - In the L/O it is NOT mandatory to buy at a specific time. However, the option money would be forfeited. In a L/P, it would be mandatory to buy.
The possible drawback or benefit... is setting the price now- If prices increase, you win- if prices decrease you could lose.
In a true lease option, "option" money is given to the seller- that is the cost of reserving the property.
Here is a description of what I mean.
Like in just about all contracts and negotiations; nothing is etched in stone [ALMOST NOTHING] you can carve out a deal that suits the seller/owner and tenant/buyer with the terms and conditions that are agreeable.