Throughout most of their time at Hogwarts, Lily Evans and James Potter seemed about as far from "soulmates" as two people could be. Lily had no love for James and his pompous ways in their early years, and James went about wooing Lily (read: ruffling his already-ruffled hair and playing catch with a Golden Snitch) in all the wrong ways.
Unfortunately for fans, we only got to know James and Lily, and therefore their relationship with each other, through recollections of the past by magical means and through memories shared by loved ones and friends of the couple. While we know the love Lily had for her son is ultimately what saved his life and led him down the path that would have Harry saving the wizarding world from darkness, we never got to explore as much of James and Lily's love affair as we would've liked. Even Harry himself at one point wonders how two people who seemed to hate each other could have come as far as they did.
"The Patronus often mutates to take the image of the love of one's life, because they so often become the 'happy thought' that generates a Patronus."
However, in the glimpses we get to see of Lily and James after they've passed, they stood united as parents in their love and support of Harry, and we know that James harbored feelings for Lily long before they were actually together. Were Harry's parents truly soulmates? While their short lives were ill-fated, was their love something that perhaps lived on? According to J.K. Rowling, the answer lies in the Patronuses of both Lily and James.
Years ago, a fan asked Rowling a poignant question: was it mere coincidence that James Potter's Patronus was a stag (a male deer), while Lily's was a doe (a female deer)?
The author of the series answered simply: "No, the Patronus often mutates to take the image of the love of one's life, because they so often become the 'happy thought' that generates a Patronus." So there you have it. Lily and James weren't just parents, they weren't just a young married couple fighting against the darkest wizard of all time — they were also, maybe most significantly, the loves of each other's lives.