If you don't have anything important scheduled the afternoon before the flight or the early morning after the flight, I would go for the early bird, arriving in FRA around 6 a.m. That's midnight east coast time, so you probably wouldn't be in bed anyway. You have the comfort of not being too tired on board which I think is luxury if you are not able to sleep and from my experience, you won't sleep in LH Y on such a short flight. You can easily stay up, eat or don't eat, that's up to every body (I have to say the hot asian/indian vegan meal is not bad at all but honestly the only eatable LH Y food but you need to reserve it in advance), watch a movie or read but you don't have to sleep and from my experience, you won't be the only one who is staying up.
As soon as you arrive in FRA in the early morning, you won't be that tired any more. This will come during day