The term Lineage may refer to the now-defunct practice whereby Avout had control over a "dowment" and could pass this control down to heritors. In effect, it allowed the Avout to own property and pass it down, even though property ownership was forbidden. Even this loophole was closed in the Third Sack.
It also commonly refers to the Old Lineage a secret extra-Mathic group, including many Edharians which had activities in the Saecular world and association with the Foral family.