Let's assume you buy the solar panels for $20,000 with a 10 year loan. You would claim the credit one time, in the year they were installed, for the full purchase price not counting interest ($20,000 in this example), even though you have not actually paid the full $20,000. Then you don't claim anything extra in future years for the monthly payments.
I don't know what your terms are, but with a traditional car lease, you are "buying" the portion of the car that you will use. For example, suppose you have a two year lease and the cash price would be $40,000. You might finance $15,000 for two years with a residual value of $25,000. That means you are "buying" $15,000 worth of the car, and you can either turn in the car at the end of the lease, or buy the other $25,000 if you want to keep the car. But you don't actually own the car for those 2 years, the lessor does.
Assuming the solar panel lease is the same thing, then you aren't buying the solar panels in a way that is eligible for any federal tax credits, because you aren't buying the panels, you are only buying the right to use them for a certain number of years. The lessor still owns them. (At the end of the lease, would you have the option to buy them or have them removed?)
If this is a purchase agreement, you claim the purchase price in the year the panels are installed, regardless of when you actually pay. And you only claim the purchase price, not the interest on any loans.
