By the time we get to Act III, scenes 2 and 4, recent events have caused King Lear to go mad.
At the beginning of scene 2, he is challenging the storm to "do your worst". The storm is also mirroring the old king's mind which is in turmoil. His thoughts are short. His language is broken. He is having trouble wrapping his mind around the idea that both Goneril and Regan have betrayed him.
He has given away his crown. He has lost his daughters. Now that he is no longer a king, having ruled most of his life, he has lost his identity.
In scene 4, he tells us,
This tempest in my mind
Doth from my senses take all feeling else
Save what beats there: filial ingratitude
It is also in this scene that Lear feels compassion, perhaps for the first time, of some else's suffering when he tells the fool to enter first. He quickly reappears followed by Edgar disguised as Poor Tom, a piteful creature. Lear sees that he is basically naked, except for a loincloth, and begins to realize that stripped of robes of power and rich clothing man is nothing but "...a poor, bare, forked animal..."
When Gloucester trys to help him, he only wants to talk to the "philospher", Poor Tom. Kent tells Gloucester,
Importune him once more to go, my lord.
His wits begin t'unsettle.
At the end of the scene, in his madness, Lear is quite childelike and once told he can bring Poor Tom, he allows Gloucester and Kent to lead him to a safe shelter.