Starfox
Hero
One-handed strength because it's wielded one-handed. I figure if you can get two-handed strength bonuses wielding a one-handed weapon with two hands, I see no problem or inconsistency getting just the one-handed bonus wielding a lance with one hand.
It is not a one-handed weapon. It is a two-handed weapon that a special rule lets you use in 1h. At least that's what I found trying to read up on it. Not sure how I want it.
http://www.d20pfsrd.com/equipment---final/weapons/weapon-descriptions/lance