Nobody seems to know much about the origin of this word, except that it comes from medieval Latin liripipium, variously explained down the centuries as the tippet of a hood, a cord, a shoe-lace and the inner sole-leather of shoes. This suggests strongly that nobody has the slightest idea what it really meant.
What we do know is that the English word (on occasion appearing as liripoop, for reasons that are entirely obscure) was used for a dangling extension to the point of a medieval hood. Hoods like these were at first worn by academics as part of their formal dress; indeed a few universities still use the word liripipe for their graduates’ ceremonial sashes. Later on, liripipes became part of everyday wear on a hood called a chaperon, a word that is closely related to the modern French chapeau.
Over time, liripipes became steadily longer, sometimes down to the ankles; this was hardly practical, so the liripipe was often wound around the head to keep it out of the way. As well as longer, it also grew more ornamental as time passed. The hoods went out of fashion in the fifteenth century and liripipe became a semi-fossil word, most commonly used today by historians of fashion and the occasional academic institution.
By the seventeenth century, the chaperon had become an item of female costume exclusively. About a century later the word began to be used figuratively for a married or elderly woman protecting a young woman — a chaperone, as we now spell it. One author explained that “Chaperon ... when used metaphorically means that the experienced married woman shelters the youthful débutante as a hood shelters the face”.