Does the lightning hitting the ground improve the fertility of the soil?
Not directly. The stroke is simply too quick to produce nitrogen in the soil...and it would also produce harmful by-products...such as ozone...and it would 'superheat' the soil, killing beneficial microbes. In the air, however, the heat of lightning can generate a chemical reaction combining nitrogen with oxygen. That dissolves in rainwater, reaching and fertilizing the soil. However, the amount of 'lightning fertilizer' actually reaching the soil (and plants) is believed to be relatively small.