It will take a couple of days for the process of alchemy to change your status from Blue to Silver on ba.com. After this time I believe your Silver Status will show up on your boarding card. If they ask to see your card in the lounge I'm sure your explanation that you just got qualified for Silver will suffice. However, this all relies on the Silver status showing up on the boarding card; you might want BAEC to fax you while you are in LA (if that's possible) to confirm your Silver status. You can then show this to the lounge dragon if necessary.

FlyermanES