Unless those contactors have the line-side wiring tucked back where it can't be seen, it looks like the builder may have forgotten to jumper the power from the ballasts from one contactor to the other. It's hard to tell what the hell is going on but it appears that he is only switching one leg of the power to the lamps since the neutrals are all spliced together on the left side, which would give you the goofy voltage readings when the lamps aren't working.
Is that unit installed upside down, with the ballasts feeding into the bottom of the contactors, and is that supposed to be a 6-ballast flip? If yes to both of those, there should be jumpers between the 1(L1)-1(L1), 3(L2)-3(L2), & 5(L3)-5(L3) terminals on each pair of contactors so that the ballasts will feed both sides.
Is that unit installed upside down, with the ballasts feeding into the bottom of the contactors, and is that supposed to be a 6-ballast flip? If yes to both of those, there should be jumpers between the 1(L1)-1(L1), 3(L2)-3(L2), & 5(L3)-5(L3) terminals on each pair of contactors so that the ballasts will feed both sides.