King Lear's tragedy comes full circle with the death of Cordelia. Consider that the King was tragically disappointed when he discovered that his daughters really did not love him.When Cordelia refuses to be phony like her sisters, and the king gets angry at her, he loses time with her, time he can't get back.
Once King Lear discovers that Cordelia, a daughter he previously overlooked, really loves him, the pain of losing that which you longed for and did not know you had, when it is taken away, the grief is double. First for the fact that he did not see her loving heart because he was blinded by his arrogance, and second for all that will never be because of her untimely death.
In the end, he realizes that Cordelia's love is all he wants out of life, he would rather go to prison with her than rule without her. That is how important Cordelia is to the King. Losing her is more than he can take, a full and total tragedy. Losing the precious moments of being loved by a sincere daughter is overwhelming.