The phrasal adjective meaning strict in behavior or morality is strait-laced, not straight-laced. Strait-laced uses an archaic sense of strait—namely, narrow, constricted, or fitting tightly. It’s possible to imagine where straight-laced might make sense (for example, in contrasting straight laces with curved ones), but we imagine such instances don’t come up often.
When first used in the 16th century, strait-laced referred to tightly fitting corsets. This doesn’t mean much to us today, so many writers assume the word is straight-laced—for example:
Jeffrey Nordling plays straight-laced FBI agent Larry Moss on the current season of the Fox hit series “24.” [North Jersey]
Offstage, she’s a straight-laced mom raising a 12-year-old daughter, Cicely. [Miami Herald]
And these writers use the more traditional spelling:
This movie is about a bunch of strait-laced guys who hit Vegas for a bachelor party. [Screen Junkies]
Janzen’s parents are a great advert for strait-laced Christianity … [The Guardian]
Most dictionaries recommend the hyphenated strait-laced over straitlaced, but the one-word form is common in U.S. publications.

