As Patti says, it depends in part on whether it's a lease-purchase agreement or a lease-option (to purchase) agreement. I'm not a lawyer, so this isn't legal advice. However...
But there are a number of different possibilities if both the buyer and seller agree. For example, if they agree, the agreement can be extended for a period of time. This might or might not be accompanied by an additional option fee, or a readjustment of the price.
For example, Joe wants to buy Sally's house. Sally agrees to sell it to Joe in 2 years for $300,000. Joe's been leasing the property, and everybody's happy. However, at the end of the 2 years, for whatever reason (low credit score, rising mortgage rates, etc.) Joe is unable to buy. They might agree to extend the agreement for another year. Period. Or they might agree to extend it for one year if Joe pays, say, $1,000, for an extension. Or they might agree to extend it for a year if Joe agrees that the new purchase price is $310,000. Any of these are possibilities if they both agree.
Or say interest rates have gone up, and now Joe can only qualify for a $290,000 mortgage. Sally could agree to sell the property to Joe for $290,000. It's all negotiable.
As for whether lease purchase agreements are binding... A lease-option is a unilateral contract. A one-way contract. The seller must sell to the buyer, if the buyer elects to exercise the option. However, the potential buyer does not have to buy. He has the right, but not the obligation, to exercise the option.
In a pure lease-purchase agreement, in which the buyer has agreed up front to lease, then to buy, there is an obligation to buy. In some cases, all the documents necessary for the purchase will be signed and put into escrow. If the buyer is unable to buy, then the terms of the purchase agreement come into play. For instance, if the agreement contains a provision stating that they buyer must be able to obtain financing or the deal is null and void, then that provision comes into play. However, the buyer can't simply change his mind, any more so than a buyer in a straighforward purchase can.
Hope that helps. Again, I'm not a lawyer; definitely see one if it's appropriate.