Here is information from Isaac's Rev. War pension file.(NARA M804. Revolutionary War Pension and Bounty-Land Warrant Application Files. Roll 1529. New York, Pension Number: R. 6181. Accessed at Fold3.com, 2 July 2016)
On the pension application he filed on 27 Oct 1835, Isaac said that he was born in June 1766 in Duchess County, New York, and that he was 69 years old "June past." (He said his birth was recorded in his father's family bible, which was then in Isaac's possession.) At the time he made his application, he was living in Clark County, Illinois.
He entered military service May 1782 (probably the 2nd of May), a month before he turned 16. He said that the militia unit that his father was in needed another man. He entered service at a place called New Brittan, NY, but is now called Canaan. The officers of his unit were Capt. Ebenezer Cady, Lt. Sluman Walttes(sp?) and Ensign Ezra Davis, and he was in a regiment commanded by Col. Waterman, Major Martin Bebee, and possibly Maj. Nathan Warner. They marched to Red Hook and then to Fish Kill. He went home when his 9 month term of service expired. Although he was given a discharge paper, he couldn't recall what happened to it.
After the War he resided in NY. "Sixteen years ago come November next" he removed to Madison, Indiana, where he remained for 3 years. From there he removed to Clark County, Illinois, where he had been ever since.
There was apparently no Roll of service for the New York militia, and Isaac's application was suspended for further proof.
There was an Isaac Lathrop from New York who served for 24 days from 8 Dec 1776 to 31 Dec 1776 in Capt. Josiah Keith's company, Col. Daggett's regiment in Massachusetts, He died in Clark County, Illinois in 1843, and he applied for a pension from Clark County, Illinois. That Isaac was from Easton, Massachusetts, and marched to Rhode Island. It doesn't sound like these are the same men.(''Massachusetts Soldiers and Sailors in the Revolutionary War,'' Vol. IX, page 541 Mass Soldiers)