Another way to consider that interesting relationship is in terms of the earlier meaning of “humour,” which still had sway in Shakespeare’s time:  a humour was one of the four fluids of the body (blood, phlegm, choler, and black bile), the dominance of which was thought to determine the character of a man; another meaning of “humour” pertains to the personality or disposition or even character of a person.  “Fortune,” furthermore (in Shakespeare’s time) might, rather capriciously, give a person a good humour or a bad one and in this way determine his fate.  For this reason, we might wonder whether Lear’s downfall results from the “humour” which fortune gave him to begin with, especially since “fortune” is a dominant motif in the play.  Pulling together all of these threads of meaning, the “cruelty of humour” can also translate to the cruelty of fortune, which is one way to understand the sometimes senseless suffering, especially in the death of Cordelia, that is part of this play

If you go to the link below, enotes provides an essay by P. Pick where he examines the comedic elements and structure of King Lear. He says the Fool is the "obvious focus of humour" in the play, noting that some of his jokes are funny, but that his humor is harsh and biting. Pick feels the most obvious example of "the humour of cruelty" is in the subplot involving Gloucester and Edgar. He also points to Kent's series of insults as a "considerable comic force". This occurs in Act II, scene 2, lines 13-20.

I think if you read the whole article, you'll find a good deal of what you're looking for to answer your question.