These are not lemons. The first car I bought this way is up to 208,000 miles. My son is driving it now. My current car would have been about $25,000 new, but I paid $15,900 for a one year old car with 20,000 miles on the odometer.
Both of those cars were former rental cars. My husband's truck was a formerly leased vehicle with 30,000 miles.
You are quite lucky! As someone who has been driving rental cars for over 9 years, they are the most beat upon cars on the road.