R elationship

Their Canon relationship?
From what has been said in the books, we know for a fact that Lucius and Severus are friends. While if they are very good friends hasn't been said for sure (it has been heavily implied by other characters), we do know that these two men know each other, maybe they even met each other when they were at Hogwarts.

My personal stance on their relationship?
I like to believe that they are friends with benefits. One uses the other for recognition, while the other uses the other for knowledge. I'm sure you can guess which is which here. I like to believe that they are rivals as well, they just haven't told each other yet. They are so Slytherin that they could actually 'dance' around each other and make the other believe something that isn't true. A false sense of friendship and familiarity.

While I don't believe these two ever had been lovers in canon, fanon changes my perceptions quite a bit. Just like I tend to think that they use each other for some things, there are other things they could also be willing to take from each other. While I don't believe there's any romantic love between these two (in fanon), I do believe that these two use each other in the sexual sense (in fanon).