The best entry point to understanding the meaning of this tragedy is to look up every instance of the word "nothing" in the text. It will appear more than 15 times. Then note the events that occur at the same time or immediately after the utterance of the word "nothing". In all but one or two cases, what happens is not "nothing" but a big "something".
So we know that this play is about "big somethings" and "little nothings" and the fact that most of the people in the play mistake little nothings for big somethings and vice-versa. For example, the wearing of regal clothing, the attendance to the king of a knightly retinue, the swearing out loud of filial love. And from that we can see that this play is trying to show that reality is internal, rather than external.
And then we can follow the king as he loses all of his external trappings, even to the point of losing his sanity on the moor, purging himself of his pride and dependence on those "little nothings" that he put such value on previously.
At the end he finally understands that everything he thought was important was actually unimportant and what he thought was unimportant was actually important. But it is too late. Shakespeare was convinced that the job of the king was to keep his country unified and healthy (cf. Hamlet). But King Lear gave his country to his children who started a war to gain control. That is the worst of his sins and he must die for it.