I am self-employed and leased a new vehicle last year. Can I report the fees paid for the down payment and other charges due on delivery? I am using TurboTax online.

Yes, you can claim fees related to leasing a vehicle, but if you used the vehicle for personal use, then you can only claim a portion based on how much you used it for business. You also must prorate the amount over the length of the lease.  ex:  if your lease is for 5 years, claim 20% of your down payment per year.