At appears that United are passing their gates at LAX T6 to American from 27 October and United is closing their United Club there on 27 October.
On 24 September their Premier check-in in T6 will be closing, and United will only operate from T7 and T8 at LAX from 27 October.
Their other move here is that the First Class Lounge will be re-branded as a United Club in October, presumably to accommodate those people who had been going to the T6 lounge. In my experience both current lounges are very busy and so this is a good move, especially as there are limited First Class international destinations from LAX these days.
UA’s Terminal 7 at LAX: