The reign of the Lancasters was eventful but short-lived. The Henriad covers the dominions of only three kings, the first of whom was no Lancaster but rather of the Bordeaux Plantagenets. When Henry IV, previously Henry Bolingbroke of Lancaster, took the throne in 1399, this began what is considered the first ‘properly English’ dynasty as opposed to the French influence which had dominated since the Norman invasion.
William Shakespeare’s other major historical tetralogy covers the reigns of Henry VI and Richard III over the course of the War of the Roses. Henry VI would be the last Lancastrian king of England: deposed, restored, deposed again, and murdered by his deposer, Edward IV.
Thus the Henriad documents the rise of the Lancasters and their peak with Henry V, though the end of the final play hints at the fall from grace soon to come. I have linked a simple timeline of major historical events covered by the tetralogy that will add context for following posts.