I flew back form LAX last month in WTP. There was a separate "express" lane for those who'd done OLCI. Much shorter but time-per-pax was still very slow. Took about 45 mins to check in then was sendt to wait another 20 mins or so to hand the bag over to TSA for baggage screening.
Luckily, the security checks after passport control were prerry quick, but it took about 1:45 from arrving at the terminal t arriving at the gate.
I would hope that Club would be faster at check-in, but you then stil end up in the same TSA line as everyone else.
As an aside, thee were big notices regarding airport renovations at LAX, including "new, behind-the-scenes" bag screening. Seems they've finally caught up with what everyone else has been doing for years, which should help simplify things when it's complete.