And isn't it ironic?

Irony is... tricky. There's several varieties of it and it's easy to get confused about what is and isn't irony. So, let's get some definitions going (for your sake and mine)

Dramatic Irony: Irony caused by readers knowing information that characters do not

Verbal Irony: A figure of speech (often sarcastic) that describes something opposite to how we normally would

Situational Irony: When readers are expecting one thing to happen, but a completely different thing does.

Act 2 scene 2 of Shakespeare's King Lear contains examples of all three forms of irony. Kent's ark in this scene is an example of situational irony. Kent, a man of the law fights with Oswald, a greedy schemer. In this case, one would expect Oswald to receive punishment for his deeds against the king; but Kent is the person who winds up in the stocks. This reversal of who sees the consequences for a crime is super ironic.

This scene also contains a nice example of verbal irony. When Kent's fate is being debated bby the various and sundry nobles, Cornwall refers to Kent as "You stubborn ancient knave, you reverent braggart" (Shakespeare II, ii 136). This is line is ironic for a couple reasons. First, Kent is old, but saying he is "ancient" is a huge overstatement by Cornwall. If Kent is "ancient" then his master Lear must predate the dinosaurs. Second, the two words of the phrase "reverent braggart" have polar opposite connotations. Someone who's reverent is very devoted; but a braggart is someone who endlessly boasts. In this line Cornwall uses a positive term (reverent) to describe how terrible he thinks Kent is. This reversal of connotation falls squarely into the camp of irony.

Cornwall's line also demonstrates the dramatic irony of scene two. He calls Kent a knave and treats him like one. None of the characters in the scene know that  Kent is actually a nobleman  in disguise. Thinking Kent a mere servant, all of the characters are willing to treat him as something lesser than them. But the good folks in the audience know that Kent is actually a knight and that he's doing the right thing by stopping Oswald. 

This my dear friends, is truly dramatic irony.

All of this irony has major implications for the play's setting. The biggest of these is that the setting of King Lear is a place of  endless reversals and confusion. Nothing is what is seems and everyone has their secrets that they hide. Another implication is that there's lots of corruption in Lear's kingdom. The criminals go free while the king's messenger sits in the stocks for goodness sake!