What justice is there in King Lear - natural or otherwise?

Yes to Justice: 

Ciclical images, which would suggest things are coming full circle within the lives of the characters. From the top of my head, I remember the line: wide skirted plaines' to describe the land in Lear's Kingdom

Another character, regularing refers to the 'wheel of fortune' and how he hopes it will turn in his favour. This suggests there is a natural justice in the world, that will find its way eventually.

In the National Theatre production of King Lear, which I say many years ago, I remeber there being a prominent circular stage, with a wheel that turned throughout. I think this would reference the the circular plot, and how justice is eventually served. 

Lear reverts back to a childlike state: suggesting the plot comes full circle and Lear is made to pay penance for his cruel actions. 

No to Justice:

Much of King Lear exists in a void, null world ('nothing comes of nothing'). When Cordelia dies, we come to see the world as entirely futile and hopeless. How can justice even begin to exist in such a nihalistic world. When King Lear walks on stage with Cordelia's dead body and cries 'OOOO', the empty sounds add to this sense of nothingness, futifility and lack of justice. 

-- This answer is entirely of the top of my head, not having looked in detail at King Lear for over 2 years.