If Lunala uses its "Lunar Pain" attack on a Pokemon that already has two damage counters on it, does it place four more damage counters on that Pokemon for a total of six?
No, that's not now it works. Lunar Pain counts how many damage counters are already on the Pokemon and places the same number of additional damage counters on it. So in your example a Pokemon with two damage counters would now have a total of four on it, not six.
Lunar Pain