Can somebody explain the basis for the Lyft lawsuit?

No. They can use the deductions against business income on Schedule C.

This is separate from the Standard Deduction, and can be taken in addition to it if the business has a loss. If the business has a profit, it can reduce the taxable amount. So if you make $1000 as a driver, you can deduct your mileage directly to reduce that number. You just have to keep a record of mileage.