Washington died in 1799. He was relatively young, as Washingtons tended to die young and it is believed to be epiglottitis complicated by blood-letting and just the basic medical knowledge of the time. I doubt being a king, or president-for-life, would make a difference to his death by more than a couple years either way (he could very well die earlier if he insisted in leading troops against a war with Pennsylvania along Braddock's Road because he knew the terrain to and around modern Pittsburgh and up to Erie, PA is one instance).
One interesting possibility though I don't know how great it would be, but it would be fun is this- In OTL Henry Lee III makes one of the greatest eulogy about Washington "First in war, first in peace, and first in the hearts of his countrymen". Let's say Washington had made some hints that Lee was a front runner. And then Lee still makes this great passionate eulogy. Lee is probably certain to be elected president for life. If he is... he has quite the talented son... Robert E. Lee. Now in OTL Henry Lee III died when Robert was very young (less than 10), had money issues, left the family and I doubt Robert grew up with any memory of his father. In this ATL Henry would be king, would have no money issues, and I assume would be a better husband and father simply for appearances sake. Robert E. Lee may not be the man we know from OTL Civil War, but he may make a good third "president for life" and begin the transition from an elected monarchy to a hereditary position. A possibility maybe someone would want to play with and see how history unfolds.