Carbon 14 decays into Nitrogen (14) by beta-emission (going from 6 protons, which is what really makes it Carbon in the first place, to 7 protons, which makes it Nitrogen, as one neutron gives up an electron to become a proton).
More 14C will make something seem younger, not older.
The rate of decay of any radioactive element is a constant particular to that isotope. The half-life is the time for half of what ever you started out with to decay. It doesn't matter how much it was; half will be gone. In the case of 14C, that half-life is, as you stated, around 5730 years, and does not change. This last point is just a clarification of your statement.
But your main point, that lightning isn't going to create the next Lucy, is accurate. Something alive would need to spend a lot of time in the near proximity of lightning for there to be any such effect through normal absorption. Simply isn't going to happen outside of Frankenstein's lab.
But the ratio between C14 and normal Carbon will decline on a curve, not linearly due to half life. If I start with 1024 marbles and every day somebody takes away half of them the sequence would be:
day 1: 1024
day 2: 512
day 3: 256
day 4: 128
day 5: 64
day 6: 32
day 7: 16
day 8: 8
day 9: 4
day 19: 2
day 20: 1
Between day 1 and 2 I lost 512 marbles. Between day 19 and 20 I only lost 1. Thus if I chart the number of marbles divided by some constant denominator or any other constant unit, I will have a curve that declines more quickly and than slows its decline. The half life is a constant sure, but the half life is the second derivative. The first derivative is not constant.