A Human heir wakes with no core and no remembered life. The lineages are Human: people of the Hallow with no core. The Covenant does not bind them into the world with a shard, because they already belong to it. Their power is the will: resolve practised until it holds under fear, hunger and temptation, and becomes a foundation of its own. The Skybreaker cultivated that foundation long ago.
An art can be held in a will as well as a shard. The five Plain arts, Banner, Reaping, Warding, Lasting Shape and Weaver's Call, are the will's home, trained at ordinary effort. The will has no affinity, so an affinity-bound art takes greater effort. No art belongs to the lineages alone.
A lord does not return. Tellan, the Keeper of Tallies keeps each lineage's name and songs on the Mnemoliths. At the recasting a new heir inherits them, sheltered by the Newcomer's Grace, with no memory, trained will, property or mark. The songs say the lineages descend from the Skybreaker. Where they truly began is unknown.
Humans have no casting core and cannot cast spells.