Lilly was very happy knowing that William put his loved ones above anything in this world. She was like that, and even her family, including Robb, were like that.
They were someone who would tear apart anyone who even dared to have thoughts about their loved ones. Even if they had to sacrifice everything, they would if it was for their loved ones.
Dragons are very protective in nature, after all. They are very few in number if only dragons with pure Bloodlines are counted. That's why they tend to be very protective of their kind, not to mention their loved ones.
Phoenix were the same as dragons in this regard. They were even fewer than dragons. After all, dragons still had many members like flood dragons and many species having impure dragon Bloodline.