The Lord Burner was the Lord President of Gallifrey’s personal temporal assassin who “burned” people from history. Irving Braxiatel claimed he served as the Lord Burner under Lord President Pandad VII, who ordered him 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.
In an alternative timeline, The Doctor 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 during his sixth incarnation. The outcome resulted in his reintegratedition 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. (Disassembled)