The initial high temperature and pressure inside the lightning channel cause the oxygen in the air to react with the other gases.Nitrogen, which makes up 78% of the atmosphere (see Chapter 1), oxidizes inside the ionized lightning path to become various oxides of nitrogen (NOx). During rainout, the NOx can fall as acid rain (nitric acid), which hurts the plants and acidifies streams and lakes on the short term. But over the long term, the NOx rained out can help fertilize the soil to encourage plant growth.
Even the oxygen molecules (O2) can be oxidized within the lightning channel to become ozone (O3), which we smell in the air as a sharp or fresh odor. Sometimes this odor is carried down and out from the thunderstorm by the downburst and outflow winds, which we can smell when the gust front passes just before the thunderstorm arrives.
Because of all this oxidation, we can say that lightning causes the air to burn.