The Lord Commander is a rank found in several of the Seven Kingdoms' institutions. It is a combination of "Lord", meaning that the person holding the title is of noble birth, or at the very least knighted, and "Commander", indicating a position of authority and leadership. The term may refer to:
The leader of the City Watch of the Seven Kingdoms' various cities is a "Lord Commander" when of noble birth, or a "Commander" when not. Janos Slynt was merely a "Commander" due to his lack of noble birth, but was later elevated to the nobility as Lord of Harrenhal in gratitude for his service to King Joffrey in betraying Eddard Stark.
In contrast, the leader of the Kingsguard is always called "Lord Commander", though this might simply be because most knights tend to be noble-born. Even if a commoner is knighted for bravery on the battelfield but was not born noble - as was the case with Ser Duncan the Tall, who was born in the slums of Flea Bottom but later became Lord Commander - being knighted technically promotes a commoner into a "noble". Members of the Kingsguard are supposed to exclusively be knights, and thus even a common-born member such as Ser Duncan would be called "Lord" Commander on the grounds that he is at least a knight. The City Watch only runs into this difference because unlike the Kingsguard, non-knights and commoners can join it and rise to command positions.
Sandor Clegane's appointment to the Kingsguard was considered controversial because he wasn't even a knight, which was explicitly against the rules of the order. The Lannisters did offer to knight Sandor, but he simply refused, because he always considered allegedly honorable knights to be hypocrites. Ultimately, Sandor abandoned the Lannisters and the Kingsguard during the Battle of the Blackwater anyway.
Ser Loras Tyrell briefly served as Lord Commander of Renly Baratheon's Kingsguard until the group's disbandment following Renly's assassination.