hello

I will be flying into LAX on TG in the evening (7ish) on an SA business class awards flight. I don't fly out until the next day (morning, around 7).
My flight out next day is within North America, on a United flight. they weren't able to get me booked into 1st class, but I know technically this ticket is considered that since I'm paying for a full business reward.
Is there any lounge that I have access to in LAX where we can stay overnight, or that is open late?
Also, would appreciate advise as to whether we should leave TBIT and try for the UA lounge as mentioned earlier in the thread, and if we're 'able' to try for the UA lounge, even though they couldn't confirm me a first class seat.
Thank you