What is my coverage under the NYS lemon law?

I recently purchased a used car from a dealer recommended from a friend. The dealer and CarFAX claimed that the vehicle passed inspection, but after driving it and hour and a half back home, it ended up stalling. I was planning to take it to my mechanic to get it checked out, but I didn't make it that far before it gave out on me. A mobile repair mechanic ran diagnostics on the vehicle (2004 Ford Escape) and found that the throttle position sensor was busted and a cylinder (4 cylinder vehicle) was misfiring, likely due to bad spark plugs. The dealer never gave me a warranty (as warranted by the NYS lemon law) before or at the time of sale. Is this dealer liable to repair these parts regardless?

Used car sales are "as-is" unless a guarantee or warranty is provided in writing. Lemon laws don't apply to used cars. So, unless the dealer is willing to help you out of the goodness of his heart, you're out of luck.

BTW, the time to get a mechanic to look over a used car is BEFORE the sale.

New York Lemon Laws cover used vehicles under the following conditions:

The vehicle was purchased, leased or transferred after the earlier of 18,000 miles or two years from original delivery; AND was purchased or leased from a New York dealer; AND had a purchase price or lease value of at least $1,500; AND has been driven less than 100,000 miles at the time of purchase/lease; AND is used primarily for personal purposes.

If it doesn't meet All of these criteria, it's not going to be covered. I'm going to assume that your vehicle was over 100,000 miles. If so, the dealer isn't required to offer you a warranty.

All the things you found after the sale could have been easily found before the sale, and should have been.

Lemon laws cover, generally speaking with some exceptions, NEW cars, not ones that are 11 years old when you purchased it. The average life of a used car is 10 years before the expensive repairs start, all the more reason to have your own mechanic evaluate before you buy.

With a written warranty the things stated in the warranty are covered. Since you had no written warranty, coverage is "as is" and "Let the buyer beware".

Less than 100,000 miles. Most 12 year old cars have more.

https://www.ag.ny.gov/sites/default/files/pdfs/publications/Used_Car_Guide_2011.pdf.