How can I talk about theme of revenge in King Lear?

It is interesting that you have chosen to focus on revenge
rather than a far more important theme, which is betrayal. In a sense, this excellent
tragedy is not a revenge tragedy in the same way as Hamlet or
Othello could be described. The only character who conceivably has
a motive of gaining revenge against others is Edmund, whose state as an illegitimate
child clearly gives him his motive for being a force of dissent and betraying others, in
the same way that Don John betrays others because of his status as bastard brother of
Don Pedro.

However, betrayal would be a much better
theme to focus on instead of revenge. Note the way that betrayal is vitally important to
the plot fo the play and how so many characters betray others. Children betray fathers
and brothers betray brothers. However, the ending of the play suggests that betrayal
automatically results in betrayers turning against each other, as Goneril and Regan do
when they fall in love with Edmund. Evil cancels evil out as they kill each other.
However, the most important example of betrayal comes when we consider Lear's blind and
foolish betrayal of his beloved daughter that sets the rest of the play in motion. This,
above all else, reminds us that blindness of some kind lies at the centre of every
betrayal.