You should not enter your lease payments under rent expenses. Instead, you should use the Vehicle Expenses categories, but your options depend on what type of 'business' you have.
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If your business is a separate entity (such a Multi-Member LLC, Partnership, S-corp and you are in TurboTax Business) then you should enter your leased vehicle under Auto and Truck Expenses. You'll be able to enter your actual lease payments, as well as other expenses. The business should own the vehicle.
Enter under: Federal Taxes > Deductions > Business Expenses > Auto and Truck Expenses
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If your business is taxed as self-employed (such as Sole Proprietor, you receive 1099-misc, or Single Member LLC and you are in TurboTax Self-Employed (online) or TurboTax Home & Business (desktop), then you need to enter your leased vehicle under Vehicle Expenses.
If your vehicle is used for part-personal, part-business than you'll be able to choose between the Actual Expense Method and the Standard Rate Method. The software will walk you through comparing your deduction. You'll only enter your lease payments under the Actual Method. The Standard Rate Method simplifies record keeping.
Note: With a leased vehicle particularly, whatever method you choose this year, you won't be able to switch in future years (until you have a new vehicle).
