I think there was something going on with Snape and Lily. As in I think he had secret feelings for her that he couldn't stand having. I reckon this is teenager Snape trying to get Lily out of his head.
Yes I know it's in black and white and people don't usually like my black and white stuff, and I also know that the actual Snape-drawing is anatomically wrong and badly drawn ...but bah to you! Bah to you all!
My favourite Lily is the smiley-closed-eyes one, even though the top one has really funky hair. As for the weird fringe things, I always picture Teen Lily with a weird seventies style, so there ya go.