There’s at least two questions in your question.
Yes a one-pay lease requires a credit check. Many people are surprised when they are denied for a one-pay because their credit profile don’t support the collateral risk. Just because you can make the payment doesn’t always mean you can lease the car.
For those with one-pay leases: what you typically see is the open trade-line from the captive for the retail lease, paid-in-full, which shows open until disposition – no impact to your DTI ratio.