(new theory coming at the end)

thoughts:
well
would it have worked? Perhaps, for a while. 
from what I know, Lily and Severus were quite close 
but could they really maintain a healthy relationship?

Hmm, well, possibly. 

I do believe that Severus would have always been drawn to the dark arts, no matter whether or not he and Lily had formulated a relationship 

I think that would eventually drive Lily away into the waiting arms of James Potter, thus resulting in the untimely death or murder of James Potter, by Severus' hand 

Whether it be Severus himself or someone sent, such as Pettigrew or perhaps Pettigrew (Peter) was sent to murder him but instead decided to let he and Lily go. 

theory: 
Severus and Lily, Lily and Snape, met up once, around ten or eleven months before Harry was born because Snape had sent her a letter, expressing his apologies and want.. or perhaps need for a reconciliation and within his letter, he claims, says or states that he has left the dark arts behind and is no longer interested. Lily believes this, maybe. Anyways, on to what is definite. Lily considers this for a while, quite some time, a considerable amount of time before eventually sending an Owl back. They arrange to meet for coffee or something, a glass of Fire-whiskey perhaps and when they do meet, they are embezzled by their drunken haze of emotions, this/their intoxication leading to the conception of Harry James Potter. 
Voldemort find out and blackmails Snape, threatening to murder Lily and their son if he does not become a double-spy for him, meaning Voldemort planned for him to go to Dumbledore and feed him little snippets of information, not too much so as to become suspect or suspiciuous, but enough to keep them in the loop and off their toes. 
Eventually, Severus does join the good-side as /once he finally realises that Voldemort does not give the privilege of having his trust, nor loyalty. 
Voldemort grows frustrated when Severus ceases to 'feed' him information and so, wand in hand, he visits the Potter residence. Upon arrival, he is met with the sight of James Potter, he murders him, quickly moving through the house in search of Lily and the infant baby, Harry. 
Once located, he begins to violently brandish his wand at Lily whilst screaming / and shouting nonsense about Severus and how she made him betray Voldemort. He also notices that a concealer charm has been cast on/upon Harry or perhaps he is too young to show prominent features. At the time.
When or as soon as Voldemort realises none of this will do him any good and that the only thing that will truly upset and get to them both, while still keeping them (both) alive is to kill their son, their infant son, Harry. Unfortunately, Lily gets in the way and surrenders her life for her son's. The rebound happens, yada, yada, yada, you know the story.

And Snape only hates and appears to scorn Harry as when, each time he looks at him or thinks about him, he can't help ponder what could have been.

Score out of ten: 
6/10 because happiness for Snape

Probability:
4/10