Elves in LOTR mate once in a lifetime; and I was kind of thinking that maybe the father(the elf in this scenario) had lived a long life, but never had he found his life mate. Feeling like there isn't much left for him, and feeling weighted by Middle Earth(sorry if this sounds goofy, like I said, I'm new) he plans to leave to Aman. Though a young human woman finds her way to Rivendell(still working out why and how) and they begin to bond. Then that kind of inexplicable connection happens, and they spend some twenty years together(I know that's short for an Elf). Remembering his concerns from long ago, she ends up encouraging him to go to Aman, not wanting him to see her grow old and die. Then yadda yadda, she convinces him, he goes, she's pregnant, has the baby.
She's forty-something at this point, raises the child for as long as she can, and then she's taken care of by the baby. Although she sent away the man she'd fallen in love with, having the child made it less painful. As for the child, it's just sort of a difficult process to live among people that age and die while they stay young. And because the child was raised with Men, it doesn't feel like it has much of a place with the Elves.
If that just sounds too special-snowflakey, I'll scrap it and go with the farmers daughter. Or maybe a hobbit.