Is "laid down" a proper term?

Looking for laid in the New Oxford American Dictionary, I noted that lay [someone] low is reported between the phrases listed under lay.

lay someone low (of an illness) reduce someone to inactivity.
• bring to an end the high position or good fortune formerly enjoyed by someone: she reflected on how quickly fate can lay a person low.

Looking for laid low by in the Corpus of Contemporary American English, I notice it is used also in sentences like

They were laid low by divorce, only to meet a wonderful new partner.

In the Corpus of Contemporary American English there isn't track of the phrase laid low from.

He was laid up with fever yesterday.

This is the correct sentence, but I can't quite explain it technically. I can't recall or construct a sentence that doesn't involve sickness. You may think of it as the fever forced him to lay down in bed and rest. (Perhaps ironically, "lay down" is right there too.)

"Laid down" has its own meaning, as in "to lay down the law" ("to establish the law, perhaps forcefully and with no room for negotiation").

"Laid up" may be related to "laid off", meaning to be fired from a job, usually due to impersonal reasons such as a company-wide downsizing.