Butchering (as we know it) as a full-time profession is a relatively new thing, so the shortest answer to your question is that there were very few just-plain-retail butchers in the 14th-15th century.

That is, of course, not strictly true: there were certainly people for whom slaughtering of animals and the jointing and hanging of meat were part of their daily work, but it would usually only have been part of the work, except in the very largest of households. Meat did not, for most people, form as large a part of the diet as it does now, so there was less demand for butchery. There is considerable variation by geography, social class, and to some degree by employment, but it's fair to say that most people would only have eaten meat every few days, or possibly only once a week. A good bit of the meat they did get would have been from hunting (either with snares, or with bows and arrows), or salted meat. Much of the protein in the medieval diet came instead from dairy products, particularly in Ireland, though notably less so in England, and eggs as well as some from beans (although these would have been fava beans, as most other kinds are from the New World, and wouldn't be available in Europe until after the 16th century) and peas. And fish, of course, which was acceptable on fast days as well as during the rest of the year.

Meat animals - cattle, pigs, sheep, and the occasional horse - were generally slaughtered in autumn, so that they did not have to be fed through the winter. Fowl of various kinds - chickens, capons (gelded roosters), geese and ducks - were slaughtered year-round, although their eggs would have kept the female birds from the knife. The people doing the slaughtering would have been the farmers themselves, in some cases, or someone among the household staff. Meat was then preserved by brining, by smoking, and by salting - the latter being the most effective and in many ways the easiest - which would hopefully last until the next set of beasts were slaughtered. And of course some meat would have been eaten fresh at around this time of year.

In the latter part of the medieval era, though, with the growth of urban populations and a corresponding decrease in room to keep meat animals or fowl, butchery began to be a retail trade - although it still wasn't just the slaughter of animals and sale of meats; it doubled up with livestock trading and even tavern-keeping, among other things. This is the era when retail trade began to be a thing at all, really - before this, many aspects of what we would regard as ordinary merchantry or shopkeeping were actually illegal. Butchers's shops were kept an eye on by the authorities, too - in times of rebellion, they were an effective source of weapons. Indeed, the support of butchers was a major factor in the Matins of Bruges (1302), the Maillotin uprising (1382), and the Cabochian Revolt (1413), to pick a few handy examples.

In this era, Lent might have been an issue for butchers - but this was also an era of guilds, and the social support that came from them. So the guilds to which the butchers belonged provided some support during the six weeks - and were powerful political groups in their own right, often among the most prestigious guilds in a given city. They would still have been involved in the trades of tanning, glue-making, and other uses of animal products, too. So the chances seem high that any individual butcher didn't suffer much hardship.

Finally, out of the scope of your question, but still interesting: it should be noted that meat consumption actually dropped by a bit during the 17th century, as populations rose. There's something of a chicken and egg situation here - New World crops, particularly the potato, helped populations to increase, but those populations then needed to be fed, and field crops are a more efficient way to feed a large population than meat.

Sources:

C. M. Woolgar, D. Serjeantson, and T. Waldron, Food in Medieval England: Diet and Nutrition
Steven Epstein, An Economic and Social History of Later Medieval Europe, 1000-1500
Fergus Kelly, Early Irish Farming
A.T. Lucas: 'Irish Food Before The Potato', in Gwerin: A Half-Yearly Journal of Folk Life, Volume 3, Issue 2, 1960
William Sayers (1994) 'Diet and fantasy in eleventh‐century Ireland: The vision of Mac Con Glinne', Food and Foodways: Explorations in the History and Culture of Human Nourishment, 6:1, 1-17
Valentina Costantini (2016) On a red line across Europe: butchers and rebellions in fourteenth-century Siena, Social History, 41:1, 72-92