To answer my own original question, LH admitted all three of us to the lounge without any issues. I don't know if it was the business class tickets or the *G w/minor child, but nobody batted an eye (after they weighed my carryons!)

The lounge was nice, the terrace was very nice. The internet was laughable--you could get 15 minutes of use *per passport*. We were there for several hours. The drinks were nice but the food was lacking unless you like really bad tea sandwiches on white bread.