Lance

From Wiki.ADnD.com

Definition for our world:
1) A sharp wooden spear with a sharp iron or steel head
2) A metal pipe for supplying oxygen under pressure
3) A thin paper tube filled with color producing fireworks
4) To cut open with a sharp knife

1ed Dungeons and Dragons
There are three lances mentioned. It must be made clear that although there is but one price listed in the equipment sheet, they are not the same weapon used from three different horses. The general ruling, although the rules do not cover the issue, is that a Light Warhorse carrying a heavy lance will only do damage as a light lance and a heavy horse carrying a light lance will only do damage as a light lance (you want best damage, then use the right lance for the horse).
Heavy lance: A weapon weighing 15 pounds doing 2d4+1/3d6 damage.
Light lance: A weapon weighing 5 pounds doing 1d6/1d8 damage.
Medium lance: A weapon weighing 10 pounds doing 1d6+1/2d6 damage.

3ed Dungeons and Dragons
There are only two lances mentioned. The official rules still do not deal with the lance/horse issue.
Heavy lance: A medium martial weapon doing 1d8 damage with a times 3 critical.
Light lance: A light martial weapon doing 1d6 damage with a times 3 critical.