As you cannot bring your car to the Island the short answer is no.
However parking is provided (ranging from free unsecured to indoor valet with plenty in between) by Sheplers or Start Line Ferry companies.
Oh dear, I gave the wrong answer earlier!! Was thinking of another hotel in Traverse City..so sorry! NO cars are allowed on Mackinac Island.
So sorry that I didn't answer sooner! The answer is yes, there is parking on site>
Sorry, I misunderstood the question, my fault. The Lake Hotel in Ireland has free Parking.
Get an answer from Lake View Hotel staff and past guests.