Not to mention all the oxygen it removes by starting fires. I further believe that lightning seldom if ever penetrates into bodies of water or otherwise does electrolysis. Falling water is not grounded and grounded water is outside the current flow, which is from the highly charged surface and the oppositely charged cloud region.
We can be sure that there was little oxygen in the atmosphere on earth until life got started, notwithstanding all the lightning. All the banded iron formations date from before the oxygen levels of the atmosphere rose. They couldn't form and haven't formed since.
This is total nonsense. If plants were converting oxygen from water at such a rate, the seas would be dropping constantly and would have almost dissappeared by now. Truth of the matter is that the earth is a very well balanced eco-system and has been so for as far back as we can tell.