Off the top of my head, the only other afternoon departures (apart from the NZ flight to London) are the Virgin Atlantic around 4/5pm and the Air France Paris flights 3/6/9pm and whenever they head for Tahiti.

The Air China flight is in the middle of the night sometime (well after the NZ5 departure to Auckland) while I've heard somewhere that a latin-american airline also contract the NZ lounge sometime before lunch... not sure which one though. TACA?

Without trying to make any explanation for the (to be honest) spotty service LAX is well known for, one possible explanation may be that the lounge is being 'wet-leased' at the time the OP attempted entry rather than being operated as an NZ lounge. I believe this is what happens at PPT.

Anyone tried the Air Canada lounge lately? I have no memory of what its like, despite being shunted there a few times when the NZ lounge was a lot smaller at LA. It must be pretty grim I guess to push AC customers into having to pull up the *A website in trying to get past the bouncers.