Lily let Scorpius guide her toward her father, not that she needed any help finding him, but it helped feeling his hand on her back. It let her know that he didn't get scared and run off yet. As nervous as she had been about the whole thing, she really wanted this to work out. She really wanted her father to see that Scorpius wasn't like the Draco he knew at that point in his life.
"It's good to see you, too, dad," She replied as she hugged her father back, then stepped to the side, watching the exchange as her father extended his hand to Scorpius.