Levi P. Morton (who was Benjamin Harrison’s Vice President) did indeed live a long life — he was exactly 96 years old when he passed away because he actually died on his birthday. Morton lived longer than any VP in history except for John Nance Garner — ol’ “Cacus Jack” — who famously said that the Vice Presidency was “not worth a bucket of warm piss.” Despite that opinion of the job, Garner actually sought it out and gave up his vastly more powerful position as Speaker of the House to become Franklin D. Roosevelt’s running mate in 1932. Garner badly wanted to be President — so badly, in fact, that he actually spent eight years in that “bucket of warm piss”. Although he almost certainly wouldn’t have been a serious contender for many reasons (especially because he was from the South at a time when Southerners still could not gain enough national appeal to even risk nominating for President), Garner felt betrayed by Roosevelt when FDR ran for an unprecedented third term in 1940. Garner retired to Texas and lived until the late-60s, dying two weeks before his 99th birthday in 1967. On the day that JFK was assassinated, one of his final phone calls was to John Nance Garner wishing him happy birthday.
As for your question, the longest amount of time between the death of a President and his Vice President was 28 years, 254 days for the Hoover/Curtis ticket. Here are the top five (which does include Washington/Adams):
1. Herbert Hoover & Charles Curtis: 28 years, 254 days
Vice President Curtis died February 8, 1936; President Hoover died October 20, 1964
2. Gerald Ford & Nelson Rockefeller: 27 years, 334 days
Vice President Rockefeller died January 26, 1979; President Ford died December 26, 2006
3. Franklin D. Roosevelt & Harry Truman: 27 years, 258 days
President Roosevelt died April 12, 1945; Vice President Truman died December 26, 1972
4. George Washington & John Adams: 26 years, 202 days
President Washington died December 14, 1799; Vice President Adams died July 4, 1826
5. Abraham Lincoln & Hannibal Hamlin: 26 years, 50 days
President Lincoln died April 15, 1865; Vice President Hamlin died July 4, 1891
And, of course, the shortest amount of time between the deaths of a President and his Vice President is about 6 hours as former President John Adams died just a few hours after his former Vice President Thomas Jefferson on July 4, 1826.