You know that old saying "the enemy of my enemy is my friend." Well, I guess while James and Severus were at Hogwarts it was similar, but more like "the guy trying to stop a guy dating the girl I like is a friend of mine because I am also trying to get him to not date her..." or something. That one kind of got away from me.
DeviantArt user Julvett, shows us that there could have been a secretly beneficial side to James and Severus' rivalry. Sure, they were competitive with one another, but when it came to Lily it had to be one of them or neither of them. I imagine that other than fighting against Voldemort, this would be the only reason these two would pair up.
It all started with a Tumblr post from dafuq-im-no-muggle
Not only do I connect to that username on a deep, spiritual level, but she also raises a great point.
From there, Julvett illustrated the situation
The two rivals meet in secret
Far away from all of their Gryffindor and Slytherin friends.
They discuss Lily's number of potential suitors
James takes care of O'Connor with his brute strength.
And decide how to knock them out of the running
And Severus gets Williams with his Half-Blood Prince potions skills.
An agreement is reached
In a shocking turn of fan fiction events, the two characters don't make out with each other. Still, it's a great story.
I love the idea that Severus and James weren't always so mean towards one another once they got a bit older. As we know, both were immature and selfish when they were young students, but they also both grew into brave, selfless men who would do anything for the ones they love.
While there's no indication that this kind of relationship between the two characters existed, I like to imagine that it did.