Snape really had a soft spot for the Malfoy family, Lily wasn’t the only one he cared for
I think we all can agree that Snape favoritized Draco in school. But the reasoning behind this goes much deeper than just him being a Slytherin. There are a few details in there that show that Snape really actually cares for the Malfoys quite a lot.
I think the beginning of this relationship came when Snape went to Hogwarts. In The Prince’s Tale, we learn that Snape is first greeted warmly at the Slytherin table by Lucius Malfoy wearing a prefect’s badge. Additionally, in Order of the Phoenix, we hear Sirius refer to Snape as “Lucius Malfoy’s lapdog”. From this, we can gather that Lucius Malfoy was somewhat of a big brotherly figure for Snape in his first year at Hogwarts. For abused, bullied young Snape, this must have planted the seeds for a deep loyalty.
In Goblet of Fire, we see another small hint. When Harry is naming the Death Eaters for Fudge in the hospital wing, he names Lucius Malfoy. Upon hearing this, Snape makes a sudden movement. We can only assume that this is Snape feeling conflicted over his old friend.
Finally, there’s the simple fact that Snape took the unbreakable vow for Narcissa. I don’t think he had to do this; why does he need Bellatrix’s trust? I think that genuine compassion for Narcissa and her family is what partially drove this.
Overall, Lucius is one of the few people that was genuinely kind to Snape at a young age, or at least was someone he admired, and this really stuck with him.