The reason James started pursuing Lily, and refused to give up on her despite constant rejection, was that on December 12th, 1972, he had what he deemed to be a prophetic dream.
He knows beyond any doubt that in the dream, he was sixty-four. He was sitting in an extremely comfortable chair of decidedly vermillion hue, with a fancy afgan hanging off off the back of it. He looked around the room, and on every wall there were pictures of his child(for in the dream he's certain he has one son, and only one son), grandchildren and grandchildren. He knows that there is a hubbub going on in the next room over, and James waits, eyes closed, and listens for footsteps.
When he opens his eyes, a white haired angel with green eyes and need of a hip replacement sweeps in as gracefully as a brittle 64 year old with arthritis in her ankles and an aforementioned faulty hip could possibly walk. She sits across from him, in a rocking chair.
Then pours in the rest of his family, first a graying man that looks to James like his father, and a woman with bright red hair. His son and his wife, obviously. Then come his grandchildren.
James dreams that he complains about their names after they all take turns leaning down to hug and kiss him. Now, he likes the names Lily and James, really he does. But, James asks his grandson "didn't you realize that the names "James" and "Lily" are intwined through the ages in a story of adventure and romance? Naming siblings "James" and "Lily" is simply asking for incest." He does not like the name "Albus Severus", though. It's the sort of name that'll get a kid made fun of for life. His grandson of that name laughs, and agrees before James starts listing names he would have prefered to Lily, James and Albus Severus. Like Vera, Chuck and Dave. Ordinary, simple names that are in no way destined for one another or sound like a Latin-bomb exploded all over the birth certificate.
His grandchildren are all adults, who are too old to be sitting on his knee, but he manages to scoop Lily the Second down on to it anyways, and he asked how the great grandchildren are doing, and why they aren't here. His little Lily replies that her husband is babysitting them all so that the increase of physical activity involved in chasing them around doesn't send her dear old grandfather into cardiac arrest.
Sixty-four year old James scoffs. He's not that old, he's still got a good fifty years in him if he lays off the Honeydukes and goes on a chocolate frog diet. After all, they make you work for a snack. Lily the Second says that Grandpa could use the work and pokes his, admittedly larger than he'd like, stomach. James pretended to sulk, and pushed his granddaughter off, to a chorus of laughter. She pouts before sitting with her siblings on a sofa adjacent to James' comfy chair.
They all talk, and laugh, and eat finger food that James swears was not there before, on a coffee table he doesn't recall having been there before. There is a lightness that the James who woke up smiling the next morning, somewhere between talking about the 2024 Quidditch World Cup and reaching for a biscuit, wasn't sure was because of the dream scene itself or the fact it was a dream. He thinks it might have been a bit of both.
Either way, he's determined to be that happy when he's sixty-four. And to do that, he must make Lily his, forevermore. The dream said so.
My sister said that every Harry Potter fan needs to write a time travel story. I decided to cheat the system. No, James didn't travel through time, he just had a scarily accurate dream, except that he was alive in the dream. If you couldn't tell, this thing is FULL of "When I'm Sixty-Four" references. To the point that I named the story after it.