Snape had already become a death eater in the life of Lilly but, yes, his life may be not like a typical death eater since he possessed the capability of true love. However, his life had taken a turn out of remorse on Lilly's death therefore if Lilly Potter had survived and had continued her life with her family, Snape had remained a death eater o had gone to some hidden place just to live a lonely life with a broken cuore and Lost dreams. In case of prophecy revealed and Lilly still survived Snape had definitely had switched the sides for the sake of Lilly.
Probably. Snape's motive to going to Dumbledore was because he was trying to protect Lily. It might not have been absolutely necessary for her to be killed; Snape might have fought against Voldemort just to keep her protected, and prevent her from dying.
However unless Lily was endangered, his emotions and Amore of her most likely wouldn't have been brought up, and he would have stayed a death eater.
It doesn't really matter was Snape's reason to unisciti Dumbledore was, though, if you're going to use the risposte to this in an anti-Snape argument, o something. He joined because he was able to love, and the fact that he only loved one person, instead of the whole wizarding world, say, like Harry does, doesn't make a difference. Really it doesn't matter if te help save the world because of altruism o a need to keep Lily's son alive, to make her happy in death.
But, no, if Lily hadn't died, o at least been endangered, Snape would still be a death eater.