One of my players is playing a mounted character, and is claiming that since a lance is a two handed weapon, that it deals double Strength damage, even when wielded one handed while mounted. While this doesn't make sense, does it follow the rules as written?
The lance does double damage if used from the back of a charging mount.
This has nothing to do with the separate rule that if you wield a one-handed weapon two-handed, or a two-handed weapon, it does 1 1/2 x STR damage (not 2x).
I will note that in Hero Lab it correctly simulates this behavior. My cavalier with a +4 STR mod, when mounted, can hold in one hand for d8+4 or two for d8+6. If I am charging, this becomes 2d8+8 one-handed or 2d8+12 two-handed.
Furthermore, this isn't some strange superheroic fighting style - before the development of the vamplate, holding on with both hands was really the only way to employ a spear or lance on horseback. Also note that lances aren't fragile or designed to break (jousting lances perhaps, but not ones made for war).
The Lance has this special quality:
Note that wielding the lance one-handed is optional. You can, not you must.
The Ride skill gives you the following benefit:
So yes, RAW you can wield a lance with two hands, while guiding your mount with your knees.
However to do so, you must still meet all the normal requirements of a two-handed weapon. So, no shield. You must be guiding your mount with your knees to have the weapon ready to strike. Etc.
Here's what the rules say about two-handed weapons:
Note that the higher strength bonus is a function of wielding a weapon two-handed, not of using a two-handed weapon. So wielding a two-handed weapon one-handed (as can be done with the lance) doesn't grant a higher strength bonus (if he wants to use a shield, for example).
(And to clarify: One-handed vs. two-handed changes the strength bonus from 1x to 1.5x. The double damage from using a lance on a charging mount is always present, whether wielded in one or both hands)
Ok consider the Lance a 2H weapons while walking but since you are riding you may get the 2H dmg but with a 1H penalty.
This is the classic (old school D&D) problem. Are all 2H weapons solely 2H or can they be wielded with 1H?
Personally if his strength check validates for 1Handing it, good, but if not then its an epic fail cause he going to ride at a penalty cause he/she has to use it with both hands and even then takes a Dex/Agi penalty due lopsiding on the horse.
Now up to date, if by some miracle of a chance the DM desides to allow for mount brackets to steady the lance even further they would still take a Dodge penalty do to the way the bracket mounts on the horse.
Lastly, since most lances are considered Thrusting weapons, as it is not being thrust but simply stationary and being driven in by inertia. They loose any dmg bonus at might incur do the lack of effort of using, so therefore any Strength modifiers would be null/void cause the player not actually using it as a weapon but more like a shield is used in a defensive position.