Lighting is the system or arrangement of lights, in a home or a theatre or film studio or wherever there are lights, or the effect that this arrangement has – “The lighting in the scene gives a feeling of doom”.
Lightening means becoming lighter in weight – “He was lightening the balloon by throwing out the ballast, and we went up, up and away!” or paler in colour – “She’s been lightening her hair again”. It also has a technical, gynaecological meaning to do with wombs: you can look that up yourselves, as I think that’s one of those terms that you will know if you need to know it.
Lightning is the visual presentation of the electrical discharge between clouds, or between clouds and objects, during a thunderstorm. As a modifier, it also means very quick, linking of course to the very quick nature of lightning itself, as in, “His lightning reflexes meant he caught the pint glass before it hit the floor”.