He was first introduced as one of Mr. Burns' many lawyers. Subsequently, he most commonly appears as the lawyer arguing against the Simpsons whenever they wind up in court. He often makes good points against them and wins over the judge. However, he has attempted to aid the Simpson family at least once. He also occasionally appears to serve as a prosecutor.
He worked for "Luvum & Burnham: Family Law" in one episode, where he had a secretary named Uwa (homophone for "YOU WHA?!?!").
His name is never stated, though it's presumably either Luvum or Burnham, given his law firm's name. In one episode, he reveals himself to be the author of a Sci-Fi novel called "The 60 Foot Baby" and on the cover he is simply credited as "Burns' Lawyer."
Despite being his lawyer, he is, sometimes, intimidated by Burns. An example of this is when Burns begins losing money, he (and Burns' other lawyers) loses his competence and acts as a yes-man out of fear of his wrath, going as far as to encourage Burns into making bad investments that bankrupt him.
In the second segment of the "Treehouse of Horror XVI", he questions what gives Mr. Burns the legal right to hunt people. He writes something that "should work in just about every courtroom" (and is then shot by Burns).
In the second segment of "Treehouse of Horror XIX", after Homer kills Krusty the Clown is approached by the lawyer and several businessman.