I may be wrong but if you are *silver or *gold you check in at terminal 6. RThis is better because you have a dedicated security line and shortewr check in.

If you want to go for a nice meal before you go on to SEA check in then go across the street and have lunch at Encounters. Its in the LAX theme building in the center of the airport. The food is pretty good and the views over LAX are awesome.

http://www.encounterlax.com/

As usual the food in the terminal sucks.

I would say that it is likely that you may leave from Terminal 7. But don't worry if you check in at 6 or 7 you can access both. They aren't really like seperate terminals, just connected wings.