There is no requirement that a lance only be used when mounted. You just won't get its 'double damage on a charge' special if you're not mounted.
3E only has so many weapon entries. If you want to use a 'spear' in one hand (and not a dinky half-spear), the Trident and lances work reasonably well as stand-in equivalent stats. If you had a character habitually using a 'lance' on foot, I'd consider it to be a 'one handed long spear' rather than a jousting lance - it'd look a little different (less silly) but be statistically identical.