Getting from the Star Alliance lounge to Terminal 7 takes 30 minutes at a brisk walking pace. They have improved the airside connection but it is still horrendous compared to other airports. Remember you have to collect your bags and clear immigration for international to international at US airports. I'm not sure how much transit time you have but this might be very tight.
Have a look at this step by step map:
I quite like the LAX Star Alliance lounge though.