AA Club Member (through Citi Executive Card) and I fly AA through LAX a few times a month. I find Tuesdays, Wednesday and Saturdays to generally be quieter than say Friday and Sundays, Oct 22nd is a Wednesday. This is especially true out of the summer. I was just there Friday afternoon this last week and it was very quiet (I was slightly surprised). My guess the lounge would be quiet enough for you.

Overall both Term 4 and 5 AA lounges are nice, except the food is mediocre at best. This last Friday it was Hawaiian chicken and fried rice as the the only main dish. Salad and humus was included for other items. A couple soups as well, Don't go for the food or less you'll be disappointed, but it will feed you. The overall lounge is nice enough for relaxing, and the bathrooms are clean and in good shape. There is always someone tending bar and AA's alcohol offering is fine, but nothing special. I enjoy the tarmac views out of both lounges.