How does leasing a car effect qualifying for a home mortgage?

An auto lease is considered installment debt, just as a car payment. Both will help or hurt your credit score (depending on payment history), and both have to be considered against your income for determining your debt ratios. One difference is that an auto loan that is almost paid off may not count on your ratios, but a lease will regardless of the time left, as lender will know you will have to replace the car/reup the lease when the initial lease is up.