The equipment is a "true lease." I pay for everything, including the payment, gas, maintenance, etc.
Legal quote of the lease:
"Lessee hereby acknowledges that lessee has been advised that, for federal income tax purposes and all other purposes, lessee will not be treated as the owner of the equipment. Lessee hereby acknowledges that the provisions of this Lease constitute a "true lease" for income tax purposes and the Lessee has no right, title or interest in the Vehicle other than solely as "Lessee" pursuant to the terms of this Lease, and that Lessee will not take any position for tax or other purposes to the contrary."
As a side note, that clause of the lease raises a 'red flag' in my mind (however, I have not read the fine print of many leases). It almost sounds like they are ATTEMPTING to circumvent Tax Law.
Let me ask you this: What happens at the end of the lease? If you have the option to buy the vehicle at the end of the lease, would the purchase price be the Fair Market Value of the vehicle?
You can use the standard mileage method to take an expense deduction for work-related miles you drive, whether leased or owned. The standard mileage method includes allowances for gas, repairs, maintenance, and the vehicle cost (depreciation or lease payment).
If you want to use the actual expense method to deduct the lease payments, you must keep track of all your vehicle expenses (including gas, repairs, etc) and all your work mileage and personal mileage, and only deduct the percentage of expenses equal to the percentage of work use. Additionally, you may have to make an extra adjustment for leased vehicles, see chapter 4 here https://www.irs.gov/pub/irs-pdf/p463.pdf
You can add tolls and parking on top of whichever method you use for vehicle operating expenses.