Labeling King Lear as a play of redemption rests in the evolution of the protagonist.
It is difficult to see Shakespeare's drama as redemptive given its ending. Everyone dies. However, if we examine King Lear himself, redemption is evident. Over the course of the work, King Lear changes. He understands that he was wrong in his beliefs. When he reunites with Cordelia, he admits his errors: "Pray, do not mock me: / I am a very foolish fond old man." In the final act, King Lear looks forward to a time when he and Cordelia can "pray, and sing, and tell old tales, and laugh." There is redemption in how King Lear acknowledges what he should deem as important in his relationships. The narrow mindedness that banished Cordelia has been replaced with greater understanding. Lear has gained wisdom as a result of his suffering, and with it, has been redeemed.
While Lear can be criticized for his actions, it is clear that he has displayed knowledge as a result of his mistakes. Shakespeare might be suggesting that this is probably some of the best that human beings can do. We make mistakes, but redemption is found when we learn from them. As Lear demonstrates, this is a painful, but necessary component of being human.