It seems unblanced to me. Why did you cut its damage in half from the standard lance? Finesse isn't a property that the designers consider requires reduced damage.
I believe the standard for melee weapons is the longsword (I saw a post calculating this somewhere)
The logic was something like this:
Base martial weapon damage is 1d8, base simple weapon is 1d6
A longsword is 1d8 and versatile (1d10)
A rapier is 1d8 and finesse, but can't ever get to 1d10
So properties acted like so (a +1 is one die size, so 1d8+1=1d10)
Heavy +1
Finesse -1
Light/Thrown 0
Reach -1
Two handed +1
This way, you get to how all weapons are on the table
-Glaive: Martial, Heavy, Two-Handed, Reach= 1d8 +1 +1 -1= 1d10
-Greataxe: Martial, Heavy, Two-Handed= 1d8 +1+1=1d12
-Dagger: Simple, Light, Thrown, Finesse= 1d6 -1/2 -1/2 -1 (1d4 is the smallest a weapon gets)
-Hatchet Simple, Light, Thrown= 1d6 + 0 + 0= 1d6
-Whip: (which is what I was basing myself on) Martial, Finesse, Reach= 1d8 -1 -1= 1d4
-Lance: Martial, Reach, Two-Handed (when not mounted), Special (since the special effect sucks it's a +2 here, [I assume, otherwise the Lance should deal 1d10) because it makes it harder to deal damage and so you deal more]= 1d8 -1 +1 +2 = 1d12
So, if we sum these up, a finesse lance would have
FL: Martial, Finesse, Reach, Two Handed, Special= 1d8 -1 -1 +1 +2 =...1d10 (I got all the way here and realized my mistake, but no way I'm gonna erase all this now)
Well, thank you for pointing out my mistake at least- I was balancing this weapon off the whip, the only other finesse reach weapon in the game so far- however, since that's what I was doing, and I didn't take into account the disadvantage at close range, my calculations were still correct, since, that would take away a +1 from the calculation.
Still, now I have to decide which version to use (although personally I would go for the whip-based one, but that's just because I have a specific build in mind.)
Anyhow, you were right, the Finesse lance would have to deal 1d10 damage if you simply work straight off the rules I listed.