It was not uncommon for medieval musicians to make their own instruments. It's possible they might have sometimes made their own catlin gut strings, as well. The process is not too mysterious: basically, sheep intestine is cleaned ( inside and out) , hammered and squeezed to crush the softer tissues, scraped. If thicker cords are wanted, it can be braided. If thinner ones, it can be cut into strips. It's hung up to dry with a weight hanging from it, stretching it out. When dry it's oiled: the gelatin in it will readily absorb moisture and make the strings soft and useless, and is also quite a good food source for bacteria and fungi, so keeping the strings from getting damp is important. But gut cords were pretty useful for other things than lutes, gitterns, violas da braccia, citoles, etc. and it's not unlikely that you could buy some gut cord from the same people who were making it for sale to fishermen, sailors....people who had nothing to do with music. It's also not likely that every lute player would have access to , and be able and willing to work in, a butcher's shop dismantling a sheep.. There were professional gut cord makers in Italy by 1216, and it's not unreasonable to suspect that there were some much earlier than that.

The more general usage was probably a problem for the musicians, because the sailors could use gut with lumps and imperfections in it for lashing something together, but those lumps and imperfections would make a string sound funny ( vibrate in various modes, some not harmonious) . For that reason, lute players complained about bad strings in the 1500's, some saying better strings were made in Munich than Italy. Likely they were complaining about bad strings long before then, and they continued to complain. When music books were written later in the Renaissance, detailed advice is given about how to buy strings, what to look for, and how not to be fooled. John Dowland had advice in his A Varietie of Lute Lessons (1610) :

wee choose Lute-strings by the freshnesse, or new-making: the which appeares unto us by their cleere and oylinesse, as they lye in the Boxe or bundle; yet herein we are often deceived, for Oyle at any time will make strings looke cleere, and therefore this tricke is too too commonly used to them when they are old.

Now because Trebles are the principall strings we need to get, choose them of a faire and cleere whitish gray, or ash-colour, and take one of the knots in your hand, but let it not be too small, for they give no sound, besides they will be either rotten for lacke of substance, or extreame false. Also open the bouts of one of the ends of the Knot, and then hold it up against the light, and looke that it be round and smooth: but if you discerne it to be curlie, as the thread of a curled Cypris, or horse hayre, (which you may as well feele as see) then refuse them, although they be both cleere and strong, because those strings were not well twisted, and therefore will never be true on the Instrument. For trying the strength of these strings, some doe set the top of their fore or middle finger on one of the ends of the Knot, which if they finde stiffe, they hould them then as good; but if it bend as wee say, through a dankish weaknesse, then they are not strong. Some againe doe take the end of the string between their teeth, and they plucke it, and thereby if it breake faseld at the end, then it is strong, but if it break stubbed then it is weake.

So, at least by the Renaissance there seems to have been a lot of trade in gut strings. Which is maybe not surprising- they would be quite light to transport and quite high-value. Thomas Mace , in his Musick's Monument of 1670, listed a variety of lute strings from France and Italy that were to be commonly found for sale by English merchants. By then, however, gut strings were having problems meeting the greater demand for more bass range, and various methods of braiding and doping the strings seem to have been tried in order to make them heavier ( it's a little obscure what these were) and so you could expect Thomas Mace to have had many more needs and many more choices in strings than Guillaume de Machaut.

Patrizio Barbieri: Roman and Neapolitan Gut String Makers 1550-1950 Galpin Society Journal ( May 2006) , v. 59 , p 147-181