Golfers don’t get this wrong. They don’t speak of a good lay (except maybe at the nineteenth hole.)

The difference between lie and lay is that lie is an intransitive verb, whereas lay is transitive.
In other words you cannot just lay and leave it at that. You have to lay something. E.g. “He lays the cup on the table.”€

I as a person cannot lay on my back. I can only lie on my back.
I can however lay carpets. (Thank you, doctorvee.)

Similarly a ball cannot lay; it can only lie, so when it is in a favourable position to be hit it is in a good lie.

Also you can see the lie of the land (its appearance, how it is lying.) Land cannot lay anything because land is not an agent.

Since cars lie beside the road in one of them, a lay-by ought, then, properly to be called a lie-by. (Except for the litter of course, which is laid; or perhaps thrown.)

Hens of course are said to “lay” because what is laid (eggs) is understood and doesn’t need to be stated. “That hen is a good layer.” (Of eggs.)

I can see where the confusion comes from because lay is unfortunately the past tense (preterite) of lie.
Compare: “Yesterday I laid my book down” (past tense of lay) and “Yesterday I lay on the couch” (past tense of lie.)

That Flanagan and Allen song always annoyed me.
“Underneath the arches we dream our dreams away” Present tense
“Underneath the arches, on cobblestones we lay.” Past tense
“Pavement is our pillow,” (present tense again) “no matter where we stray,
Underneath the arches we dream our dreams away.” Present tense.
I know it was for the sake of the rhyme but it makes no sense for the second line to be in a different tense from the others.

So did the Troggs’ – and Wet Wet Wet’s (they should have known better) – “Love Is All Around.”
“I see your face before me as I lay on my bed.”
NO. NO. NO. As I lie on my bed.

You can discover if REM did any better in this clip.

REM: Love is All Around

I suppose the sexual connotation of “a good lay” comes from the fact that you may perhaps lie on a bed to perform the act and so the phrase has arisen from the confusion. (Unless of course you were carrying your partner beforehand and laid her/him down onto the bed first.)

The post title might have brought in a few new visitors, don’t you think?
How cruel of me to disappoint them.