Lilu didn't immediately rush into the hug, though of her siblings she was the one who liked them best. Al actively despised them for the most part, and Jamie wasn't much better. However, she wanted to take a moment to studying the man she'd heard so much about, the man whose memories she now held protected. Because she would protect them. She wanted to help him, but at the same time she'd protect his secrets until he was ready to let them go.
"It's pretty brilliant to meet you too, and I don't think God Granddaughter is a thing but we can run with it." She wanted to tell him that there was nothing wrong with loving the family you were related to by blood, that it was just as important as the family you made yourself, but she reminded herself to take baby steps. "I like hugs, but I also like finger guns."
Still, she stepped into the hug and held on for a long moment. Sirius' primary love language would be physical touch, and his Animagus form was an obvious reflection of that, so she let the hug go on a bit longer than she would have with anyone other than her brothers.