Challenge for you musical detectives

When I was a teen back in 1970, There was a demo record releases that
I guess didn't do well, for it ended up in the Goodwill record bin as
a 45 rpm demo. As a hobby I would buy these unknown records (at five
cents per record), take it home to see if I liked it.

I believe it was released on the London Label and I don't know the
name of the song. One verse goes like this:

On a sunny day in Dallas
back in 1963
Four days into April
down in Memphis, Tennessee.
Two men met their fat there
Oh, no, that can't be right...

That is all I remember, but it was a really pretty song that I felt
had a message.

Anyone have any ideas?

Lady Veteran...

Excuse---that is FATE, not FAT..LOL

Liz W...

LOL!

Don't you sometimes wish you could just suck messages straight back into
your computer!! Once they're out there, you're done!! At least you got in
first...lol

Lady Veteran...

Yes, I did. They may have dealt with their FAT but it was their FATE
the song talks about.

Hope someone can find it.