House Lineacrux was an Oldblood House of Gallifrey, and often considered one of the more archetypical Time Lord Houses: a producer of old, ponderous men, obsessed with the rules of non-intervention and the Laws of Time.
The House was responsible for crypto-forming the Nine Gallifreys, perhaps creating the prominent status it seems to hold during the War in Heaven (PROSE: The Book of the War).