This exploration began with me wondering what a cavalier who specialized in fighting giants looked like. I call it the Titan Lancer. It's a Titan Fighter 1 / Titan Mauler 1 / Gendarme X. Order of the Hero works better thematically but Sword is just so good.
I see no reason why a Titan Fighter couldn't charge with a large lance but I was wondering if he could do it one handed. As ridiculous as charging into giants with a tree for a lance in one hand and a tower shield in the other is, I was wondering if this was legal or if somewhere its said that the one-handing a lance when mounted only applies to properly sized lances? Naturally the penalty for this nonsense who be a -6 to attack for what amounts to +5 avg damage (14 dmg instead of 9).
Alternatively, is it possible that the mount downgrades the large lance to be an effective normal lance for the purposes of wielding so that one could two hand a large lance without Giant Weapon Wielder penalties?
You can one-hand a Large lance while mounted (and only while mounted)--it's still a two-handed weapon for you, and there's no "properly sized" qualification that I'm aware of. Not that there would be--when the lance rules were printed, there was no way to wield a two-handed weapon sized for a larger creature. It would work as a Large weapon still, and you'd take the ridiculous attack roll penalty.