Sub-Roman Britain (Cavalry etc)

[Medicus matt]

Development of the lance in the Medieval sense, of course, depended on the introduction of the hard stirrup. Without it, the rider had to use the lance as a spear or risk unseating himself.

That's highly debatable.
Persian cavalry seemed to manage using the lance at the charge without stirrups, thanks in part to their high backed saddles and also because their lances (described as 'great pointed staffs, bigger than a spear) were fixed to horses, as descirbed by Heliodorus (who gives a splendid description of the equipment of the Persian Heavy Cavalry) in the 3rd century.

When the time of battle comes, he gives his horse the reins and spurs him with his heels and rides upon his enemies at full speed like a man made of iron or a statue fashioned with hammers. His great staff at its pointed end is tied with a cord to the horse’s neck and the hinder end is made fast to its buttocks, so that in the conflict it does not yield but helps the horseman’s hand, who does but guide the same aright. Thus it gives the greater blow and runs through every man it hits, and often carries away two men together pierced by one stroke.

Strirrups were essential in turning cavalrymen into effective melee combatants, heavy lancers could do without them.