Often, because of the similar pronunciation, misspelled “straightlaced.”
The first element was streit in Middle English, having been introduced in about the fourteenth century.
It came from the Old French estreit, “tight, close, narrow,” and similar words (Spanish estrecho, Portuguese estreito, Italian stretto) are to be found in the other Romance languages.
All are derived from the Latin strictus, the past participle of stringere, “to tighten, bind tightly.”
Lace came in to the languge at about the same time, also from the French (lacier) from the Latin laciare, “to ensnare.”
Here, too, there are closely related words in the other Romance languages.
The two words have been found together as early as 1430 in their literal significance of “tightly laced,” but the compound term is not found until the sixteenth century.
It was about at the same time that the figurative use of the term became established, for the strictures laid upon the body through the tight lacing of the bodice were quickly seen to be closely similar to those laid upon one’s conduct through what seemed to be excessive prudishness.