It very much does!

On a recent trip, the LD at the LH contract lounge I use at my home airport all the time recognized me and let us all in for free, although "by the book" we would have had to pay for the kids and explicitly said we would he happy to do so. On the same trip, the lounge of a LH partner airline denied access to the kids, as they are over 2, and didn't offer access for a fee, i.e. we couldn't use the lounge as a family, which is very inconvenient based on a stupid rule and no incentive to fly that airline via that airport again.