The Lounge at LAUS is quite far from the tracks Amtrak uses, which are generally the higher numbered tracks. To get to the Lounge from the platforms, you have to go down the ramp to the pedestrian tunnel under the tracks, walk to the "historic station"/Alameda end of it, turn left on entering the station, walk past the ticket counter, make another left at the end of it, then take the elevator or stairs up to the Lounge. It is quite a long walk. For boarding, if you use a Red Cap, they'll take you out the back door and use a cart to drive around the ends of the platforms to yours, which is somewhat shorter, but if you don't use a Red Cap, you have to go back through the pedestrian tunnel.
As I think about it, it is about the farthest Metropolitan Lounge from the platforms there is, at least as far as Chicago's and maybe farther. If your Surfliner arrives 40 minutes before the Starlight leaves, they'll be calling it about the time you get to the Lounge.
If I were you, I wouldn't even go into the station, that tunnel is pretty long. Maybe just go down into the tunnel and look on the overhead boards for 14.