Galleries North is 5am, Galleries South is 5.30. I would recommend heading through for that kind of time even for a flight due to depart at 7:20 as security tends to be a dream before 5.30 and much worse after 5.45...
Closing time - not sure - was out to HKG v late one evening last year and the lounge was definitely open until I left... probably 10.30ish