I don't think there is a simple yes / no answer to your question when it comes to whether this will work - according to T&C you can't, but that's very different to the real world.
As you've pointed out Koru access rules are that the guest has to be on the same flight as you. Domestically this is simply not enforced.
The LAX lounge is not a Koru lounge, but a *A lounge. Air NZ built and managed the lounge (but I'm pretty sure they don't actually manage it now) and Air NZ provide Koru members access to this lounge under Koru rules.
If you turn up the lounge, scan yourself in and ask nicely if you can scan a guest in you may find you have no issue. It really just depends how the agent wants to handle the guest situation.