As of right now, the Alaska Lounge at LAX does accept PP but often times there are capacity issues for members unless you're an Alaska Lounge Member. I have both but decided to be a ALM after not being allowed to enter b/c of capacity multitude of times (18>). Also, if you're an AMEX Platnium cardholder you can use you're $200 airline credit to help reimburse for your ALM membership and if you're an Alaska Airlines MVP , you get a discounted rate of $375 rather than $450. Lastly, once you join, you get speedily access by using fingerprint scanning to sign in and will be allowed to go to some of American's Admirals clubs as long as you're flying with them as they and Alaska are partners. Hope that clears some things up for you. Happy flying!
As Rory said, it really depends on how many people are in the club. I'm a priority pass member and recently showed up to find a sign posted saying that the club was full. I waited around for 20 minutes and after numerous people left, they opened the club back up to priority pass. It's a very small lounge that is fills up quickly.
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