To my knowledge, all the lounges close overnight. You'll be entitled to access the F lounge which will close around 1am, after the last TG flight. It re-opens quite early, around 5am I think.

So your options are:
(1) Check into an airport hotel (but this isn't your thing)
(2) Relax in the F lounge until it closes and re-enter a few hours later.

If you opt for 2, then you can always grab one of the recliners at the beginning of concourse C or at the concourse E end of concourse D. I've never tried these seats, but they look comfy enough judging by the number of people sleeping in them whenever I walk by. Hint: You may wish to leave any valuables in the F lounge to avoid risk of them being stolen while you're taking a nap.

I guess you could always ask the F lounge staff if they would mind you staying in one of the slumber rooms when they lock up for the night, but I think the chances of success are slim.

Happy travels.