I’m not sure bullying has anything to do with it...I speculate that Snape was just another guy totally captivated by Lily Evans... there has never been a bad thing said about her... I think we find out in the last book that Snape was devastated that he inadvertently caused her death. He doesn’t like Harry because he looks so much like James, but because he’s Lily’s son, he’s never hurt him either, he even stopped that curse in the last pages of HBP.
Less than 2 weeks till the final truth is known...
;D
I agree with that too, about him loving Lily. I think when Petunia was talking about that “awful” boy, she meant Snape, not James.
I also speculate that Snape had a thing for Lily. There's a clue in "Prince" where the replacement Potions professor, commenting about Harry's newfound talents in Potions (due to Snape's book) and how Lily also shined in Potions. Perhaps Snape has a crush on Lily and was helping her get through Potions class