I'm not saying he's bad. He'll be a loving and supportive father, no doubt. But, he might be a little too supportive to a point where it isn't quite safe for Harry. Instead of telling Harry that he shouldn't be sneaking around past his bedtime, he might be advising Harry on better ways to avoid Filch and Mrs Norris and on similar mischievous situations. Lily would be more reasonable, ensuring Harry's safety, making sure he doesn't get in too much while letting him have some fun too. And my guess is if Lily was around, Snape would have no choice but to control his mouth and actions because he wanted to make a good impression on Lily - therefore not making Harry's life too much of a living hell.
Just my guess.
