harry potter - If it wasn't for his love for Lily, would Snape have a Patronus?

Jaclyn: Did lily ever have feelings back for Snape?

J.K. Rowling: Yes. She might even have grown to love him romantically (she certainly loved him as a friend) if he had not loved Dark Magic so much, and been drawn to such loathesome people and acts.

Mugglenet - Deathly Hallows Webchat - July 2007

I think that had Lily not been in the picture, Snape would have continued down the path of becoming a full-fledged Death Eater. As J.K. Rowling has explained, Snape wanted to be part of something important, something big, because he felt insecure about himself (which was probably exacerbated by the bullying he endured from James Potter and Sirius Black). Further, the Death Eaters were compatible with his inherent attraction to the Dark Arts.

Nithya: Lily detested Mulciber and Avery. If Snape really loved her, why didn't he sacrifice their company for her sake?

J.K. Rowling: Well, that is Snape's tragedy. Given his time over again he would not have become a Death Eater, but like many insecure, vulnerable people (like Wormtail) he craved membership of something big and powerful, something impressive. He wanted Lily and he wanted Mulciber too. He never really understood Lily's aversion; he was so blinded by his attraction to the dark side he thought she would find him impressive if he became a real Death Eater.

Mugglenet - Deathly Hallows Webchat - July 2007

Lily was Snape's moral compass; without her, I think he would have become like Draco Malfoy: Able to shut down the good parts of himself and compartmentalize his emotions to allow himself to brutalize others without emotional trauma. Snape grew up with an alcoholic father and a possibly domestically violent home; without Lily, Snape didn't have a lot to be happy about.

As dlanod mentioned in his question:

J.K. Rowling: [A] Patronus is used against things that the Death Eaters generally generate, or fight alongside. They would not need Patronuses.

Mugglenet - Deathly Hallows Webchat - July 2007

I don't know how long Snape would have remained a bonafide Death Eater, but during the time that he was, I don't think he would have been able to produce a corporeal Patronus, regardless of the status of the Dementors.