I can imagine that with an overhand spear*, but underhand lances feel kinda awkward for melee, especially if you're sitting on a horse.
Anyway, I prefer to switch to maces/whatever in cavalry fights to be historically accurate (and because maces are kewl), however I've learned to my intense frustration that the RTW engine lets lances win in those situations.

*I always have overhand spear cavalry use their spear against infantry, except when they're up against armoured units.