What if before conceiving Harry, Lily spent an evening with Severus Snape, and conceived a daughter. As soon as the girl was born, Lily sent her to Severus, fearing that if James ever found out, he would never forgive her. Severus named the girl Lucila Lily Snape and raised her, never telling anyone, but Dumbledore, who her mother was.

The oddest thing?

Harry and Lucila are twins, from different father's. And you thought Snape having a daughter was weird.