<not again...>
Yes, "by the book" you can use a lance even on foot (without the extra damage for a mounted charge). And in reality, there's nothing that would stop an unhorsed knight from using his lance that way either. (Jousting armor - and presumably combat armor - has a "hook" to rest the lance into. The lance is never in contact with the horse.)
However using a lance in that way is unbalanced compared to the other weapons in the weapon table, so it should probably not be allowed without adding extra restrictions (amount of movement needed, direction of attack, multiple attacks, etc.)
The problem really stems from the fact they needed to fudge things somewhat to make the classical "lance and shield" knight possible. I don't think anyone at WotC ever considered the possibilities when using it unmounted.