I was using this term in something I was writing today, and I found I had to pause to consider the correct spelling. So, being the eternally curious person that I am, I found out more than I needed, and will share it here for those who are interested.

Strait-laced is an adjective phrase that describes someone who adheres rigorously to rules and to their moral beliefs.
The word strait originally started as a geographical term, meaning a narrowing, or a narrow passage of water connecting two seas or two other large areas of water, such as the Strait of Gibraltar.
“Strait-laced” dates from the late 1400s. It referred to a women’s clothing item: a bodice. Women wore this garment on the upper body; it was similar to a vest. It was fastened with ties or laces, with the intent of making the woman’s waist appear slender — in some cases, atrociously, unnaturally narrow. This meant that the bodice was tightly bound. (Strait = narrow, constricted, tight, limited).

Extrapolating from that definition of a physical item to behavior in general was a fairly small (and predictable) step, and that extrapolation happened in the 1500s.

But the word strait never became a common term, other than in its geographic sense and in this one term strait-laced. So it’s easy to see how the confusion with straight crept in, since the word “straight” is quite well-known and the word “strait” is not. This mistake is further enabled because the meaning of the word “straight”, in and of itself, often has the meaning of direct or honest. The “laces” part of the definition has been forgotten.

“Straight” was originally an adjective applied to something physical as well. It’s been traced back to the late 14th century, with a meaning of “direct, undeviating; not crooked, not bent or curved.” It probably derived from an adjectival use of Old English streht (earlier streaht), past participle of streccan “to stretch”. Of course, when something is stretched, it generally loses it irregularities and becomes straight.

The extrapolation of that word from a physical object to a human attribute has been traced back to the 1520s, with a meaning of “true, direct, honest”.

Other current meanings of the word straight mostly cropped up much later.

Of communication, “clear, unambiguous,” from 1862.

Sense of “undiluted, uncompromising” (as in straight whiskey, 1874) is American English, first recorded 1856.
Theatrical sense of “serious” (as opposed to popular or comic) is attested from 1895; vaudeville slang straight man first attested 1923.

“Go straight” in the underworld slang sense is from 1919; straighten up “become respectable” is from 1907. To play it straight is from 1906 in theater, 1907 in sports (“play fair”), with figurative extension; later perhaps also from jazz.
Straight shooter is from 1928 (and that usage harks back more to its etymology as a physical description of something without curves or bends.)

And those of us who lived through the 1960s know that “straight” as an adjective or a noun was the term applied to those in the mainstream, as opposed to those in the counterculture.

“Straight-laced” is an example of a spelling that has been used incorrectly so often that it has become common usage. I don’t think you’ll find it in dictionaries yet, but it could happen soon. I found many occurrences…