How does Shakespeare present the theme of justice in King Lear?

When Shakespeare began writing King Lear, a famous trial was underway, that being the case of Brian Annesley in 1603: Grace, the eldest of Annesley's three daughters, attempted to declare her father too senile to manage his estate and will. Although he never lived to see his youngest daughter Cordell win the case for him, justice was eventually served. Many believe that King Lear was inspired by this story, and that jstice fails in both the fictional and the real world (it came too late for Lear's model Sir Annesley as well as Lear himself); therefore it could be said that King Lear is actually an exploration of injustice. CJ Sisson supports this by saying "In King Lear...the function of justice itself has come into question": justice has not proved to be a useful force in the real world, therefore it shall be criticised in Lear's world.