The Lord Burner was the Lord President of Gallifrey's personal temporal assassin who "burned" people from history. Irving Braxiatel claimed to have been the target of a burn edict issued by President Pandad VII. However he killed the Lord Burner, and was punished by having the title bestowed upon him. His only edict from Pandad VII was to burn "an old man" and "his granddaughter". He disobeyed this order as they were family. The intended victims stole a TARDIS and fled Gallifrey and it was strongly implied that Braxiatel had tipped the escapees off, and arranged the later accident that killed Pandad VII.
In an alternative timeline, an incarnation of the Doctor resembling the “prime” Doctor’s sixth incarnation killed his brother Braxiatel, who likewise served as Lord Burner in that timeline. He adopted his title, stole a TARDIS and fled Gallifrey to challenge the Time Lords' right to rewrite history. He was eventually captured and placed on trial. The outcome resulted in his reintegration into Time Lord society. By the time that President Romana came to power, he had adopted the title "Lord Burner" as his official nomenclature, no longer referring to himself as "the Doctor" as he had done earlier in his personal timeline. This version of the Doctor was apparently killed in a struggle with the Braxiatel of the 'prime' timeline. (AUDIO: Disassembled)