Priest and children make sense, but why lepers? Was it a personal quirk of Philip? Fear of infection? Or broader medieval attitudes towards them?
I'm a simple man, I see "Lalaing" and I upvote.
On a more serious note, the taking of the Poeke castle was part of an expensive punitive campaign lead by Philip the Good against the Flemish towns rallied around Ghent.
Flemish towns used to revolt every 20 to 40 years or so from the 13th to the 16th century. The cycle went hand in hand with economic growth and recessions.
Back in 1436, the Flemish towns rebelled after Philip the Good made peace with the king of France and went to war with the king of England. It had serious economic repercussions on the Flemish towns because the trade between Flanders and England was cut off. It lead to a hasty peace between the duke of Burgundy and the king of England despite the ongoing Hundred Years' War. Philip the Good saved face by having the duke of Orléans liberated from England where he'd been detained since 1415. He married the poor lad to one of his niece and put to rest the old quarrel between the two houses of Burgundy and Orléans, proving that he was working, in fact, for the good of the realm.
However, the 1453 Ghent War was of another breed. The revolt, here, was a pure show of force between the duke of Burgundy, who was count of Flanders, and the major Flemish towns. Back in January 1447, Philip the Good asked the Flemish towns if he could raise a new tax on salt "on the lines of the French gabelle." (Vaughan, Philip the Good, 2002, p. 306) This request was bluntly denied by the people of Ghent, the most powerful Flemish city at the time, and the neighbouring towns (Bruges, Ypres, etc.) followed this example.
Magnanimous in the face of such an insult (I'm being sarcastic), Philip the Good tried to meddle with the municipal elections at Ghent in 1447, and then again and this time successfully in 1449. During the 1450 negociations that followed the chaotic 1449 elections, Philip the Good showed his hand. He was pursuing the suppression of several privileges long acquired by the people of Ghent by reinstating a charter dating back from 1287! The political imbroglio worsened and turned into a full-on Game of Thrones miniseries at this point up until the moment that the actual people of Ghent, and not their representatives, were fed up with the situation, took up arms and seized all the nearby castles to defend their rights.
This was yet another revolt, like there'd been many before and like there'd be more in the future in the Low Countries. Against such open threats to their authorities, lay and ecclesiastic lords had but one move: to crush the opposition. They would gather their troops, storm the land, take and dismantle opposing castles and hang every one who was captured in arms against them. It was basically a tradition at this point. It worked well against unruly urban militias and companies of bandits who elected domicile in any abandonned castle to terrorize the neighbouring countryside. A well-rounded and established method. A costly one, though. When they were faced against rebelling towns, however, lay and ecclesiastic lords usually reconciled in the end by throwing a lavish party that ultimately only confirmed their position, authority, prestige and power [see my former answer on the matter with u/J-Force contribution].
Philip the Good did what he knew best! He gathered his troops, a well-fed and experienced army of Picard knights, then he manoeuvred into Flanders to put Ghent back to its place. The year was 1453 and many places fell to the Burgundians. On June 27th, Schendelbeke fell. The Burgundians wished to control two more places in order to exert a blocade against Ghent and starve the city: Poeke and Gavere.
Philip led his army back to Courtrai on 1 July and on the 2 July he encamped at Poeke. It was here that the famous jouster and knight-errant Jacques de Lalaing was killed by a cannon-ball while he was observing the damage done to the walls of the castle by one of the ducal bombards. (Vaughan, op. cit., p. 328)
Eventually, though, Poeke fell to the Burgundians and their superior artillery. Then happened what you mentioned in your question: the garrison of Poeke, 87 men strong, was hanged. Is it, though, because Philip the Good was mad at Lalaing's death? He was certainly saddened by such a loss, but the hanging was only a common sentence to emprisonned rebels. 104 men were hanged at trees a few days earlier when Schedelbeke fell at the recommandation of Jean de Croy, Philip the Good's lead military advisor at the time. Another man was also hanged to the wings of a mill to warn the garrison of Gavere of their fate if they kept up their resistance against the ducal authority.
Now, about the lepers.
Leprosy was quite the scary disease at the time. It'd been around for longer than the Black Death (which recurred every 15 to 20 years until the 18th century, though with much less impact on the overall European mortality rate than in 1346-1353). There is talk of lepers in the novel of Tristan and Iseult, which dates from the 11th century. People were accustomed to the disease by the 15th century, though they proved quite powerless against it. They'd come up with the best solution they could thing of: the lockdown of all the lepers in a dedicated area. Lepers were not to be approached, nor to be talked to. They were to be left alone, casted aside from society but from holy men and women who were daring enough to approach them and try to cure them. It was commonly believed that their disease was a God-given curse and nobody wanted to get close to such a thing.
Moreover, disease (more than actual combat) was the first cause of death in medieval armies. Military commanders avoided to the best of their abilities the spread of diseases among their ranks. Henry V of England died of disentry, such thing striked hard and fast and spared no one. There was therefore NO CHANCE that the duke of Burgundy would send his experienced and noble knights anywhere near the lepers. They were already condemned. They were already in pain and suffering from a God-given curse. What could men do to punish them further?
The hanging of the Poeke garrison was not a reaction to Jacques de Lalaing's death, though Philip the Good was certainly saddened by it. The mass hanging of rebel garrisons and bandits was a common sentence when they were taken in combat (just like the Romans used to mass crucify slaves who rebelled against their masters). As for the lepers, they were already casted aside from society and believed to suffer from a God-given curse, nothing could be done to worsen their condition. Moreover, it would have been insanely dangerous to get any soldier near lepers as it could have spread leprosy within the ranks of the army.