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.