No, Versatile Design does not let you finesse a lance
So the word “light” is being reused here to mean two different things, and it’s kind of a chicken-and-the-egg problem.
Light as a “handedness,” so “light weapons” as opposed to “one-handed weapons” and “two-handed weapons.” Light weapons can be used with Weapon Finesse, take smaller penalties when using two-weapon fighting, cannot benefit from Power Attack, and so on.
Light as an English-language adjective in the term “light blades,” the name of a fighter weapon group. In this context, a “light blades” refers to any of the weapons found in the light blades group.1 Not all weapons in the fighter's Light Blades group are finesse-able (scizore, chakram, manople), and simply being in the group doesn’t make them light weapons.
In other words, the light blades were chosen to be in that group because they are light—but they were already light before the fighter got involved. Adding them to the fighter weapon group “light blades” didn’t make them light, they already were.
Likewise, if you add the lance to this group using Versatile Design, that doesn’t make it a light weapon. A light blade, yes, and things that care about what fighter weapon group you are using will recognize that, but it doesn’t otherwise change how the lance works. It will not allow you to use Weapon Finesse with the lance.
- Namely, a bayonet, butterfly knife, butterfly sword, chakram, dagger, deer horn knife, Drow razor, dueling dagger, gladius, hunga munga, kama, katar, kerambit, kukri, machete, madu, manople, pata, quadrens, rapier, sanpkhang, sawtooth sabre, scizore, shortsword, sica, sickle, spiral rapier, starknife, swordbreaker dagger, sword cane, wakizashi, or war razor.
However, effortless lace may let you finesse a lance
Effortless lace is a very useful magic item that can allow you to finesse weapons you ordinarily couldn’t, along with other useful properties. Specifically,
When wrapped around the grip of a one-handed piercing or slashing melee weapon for 24 hours, the ribbon’s magic permanently merges with the weapon, [so that] the weapon is treated as a light melee weapon when determining whether it can be used with Weapon Finesse, as well as with any feat, spell, or special weapon ability that can be used in conjunction with light weapons.
(Effortless lace item description)
Notice that this can only be used on a one-handed piercing or slashing weapon—a lance is clearly piercing, so that’s no trouble, but it’s a two-handed weapon. However, note also that
While mounted, you can wield a lance with one hand.
(Lance weapon description)
This does not, strictly speaking, make the lance a one-handed weapon. The rules as written would not allow you to use effortless lace on a lance.
Your GM, however, might. I would. I would allow you to use the effortless lace on the lance, but it only benefits from the lace while you are mounted.