Family is about making memories

Harry looked down at his father, who had hastily crossed out the ‘L.E.’ he had been embellishing, jumped to his feet, stuffed his quill and the exam paper into his bag, which he slung over his back, and stood waiting for Sirius to join him.

Clearly, he doesn’t want anyone to see that he’s been doodling Lily’s initials so he probably tries to be casual about the fact that likes her around people other than his friends.

“What is it with her?” said James, trying and failing to look as though this was a throwaway question of no real importance to him.

Again, trying to be casual; I really think that it’s quite possible that the scene by the lake was the first time it was public knowledge that James liked her, and even then he was attempting to make it seem like it wasn’t a big deal to him. So if that’s the case, how else would Snape know about the crush?

“I know your theory,” said Lily, and she sounded cold. “Why are you so obsessed with them anyway? Why do you care what they’re doing at night?”

Huh. Obsessed with the Marauder’s whereabouts.

“It served him right,” [Sirius] sneered. “Sneaking around, trying to find out what we were up to … hoping he could get us expelled …”

Snape spies on people?!?!? Whaaaaaat no way I mean it’s not like he’s spent his entire life doing such a thing - oh wait. We all know that Snape spied on Lily before Hogwarts, this proves that he spied on the Marauders as a student at Hogwarts, he was a spy after Hogwarts during the tail end of the First War (passing on some info to Dumbledore after Voldemort decided to go after Lily) and then a double agent during the Second War - that’s more than half of his lifetime as a spy. Dude’s for real like a professional stalker. So I’d literally put money on the fact that he probably overheard James discussing his crush on Lily or talking very highly/lovingly about her while with his friends one night while following them around.