Id say when the channel is ionized the air becomes conductor (actually the lightning is made of several small bursts that are interconnected). Given the fact that  weve got a short pulse in time domain, with accelerated charges, EM radiation occurs.

Lightning.

It is an arc discharge with rather short duration and high power density. Thease are mainly used in a more controlled way for example for welding, certain types of lamps, high voltage circuit breakers.

Arcs with duration ~ microsecond range are usually called sparks. Even shorter discharges may be created which in fact stop before they are completed in to arcs. These are also called transient discharges and have typical time duration ~ nanoseconds.

There are two methods to create these discharges.

1st method:

A dielectric layer can cover one or two of the electrodes in the discharge gap. At a sufficiently high voltage between the electrodes the discharge starts with the incorporation of gas. It spreads out until it reaches the electrodes but at the dielectric it builds up a space charge that cancel the applied electric field. At that moment the discharge stops. This discharge is usually called dielectric barrier discharge.

2nd method:

One can use an asymmetric electrode pair. Then the discharge develops in the high field region near the sharp electrode and it moves out towards the cathode. Here, there are two possibilities to avoid the transition in to an arc.

First the voltage can be made low enough to stop the spreading of the discharge somewhere before the cathode is reached.

OR  Corona discharge

One can stop or lower the voltage when the cathode is reached. In the second way more energy can be put on to the discharge but it is more difficult to make the power supply. This type of discharge is called corona. It is a positive corona when the electrode with the strongest curvature is connected to the positive output of the power supply and a negative corona when this electrode is connected to the negative terminal of the power supply.

In corona discharges at relatively low voltages the discharge stops itself due to the build up of space charge near the sharp electrode. This space charge then disappears due to diffusion and recombination and a new discharge pulse appears. This is the self-repetitive corona and it occurs in the positive and in the negative case.

You may go through literature for more basic understanding. Good luck.

In my opinion, electrical breakdown of materials (https://en.wikipedia.org/wiki/Electrical_breakdown) doesn't have the properties requested for a quantum mechanical modeling of radiation-matter interaction. It is accompanied by many complicated, highly non-linear effects involving the materials themselves. By “non-linear” I mean specifically that one cannot tell apart causes and effects. Above all, the accompanying luminous effects have none of the characteristics usually associated with electromagnetic waves, i.e. definite amplitude, frequency and phase. Perhaps, to try and understand what is happening, one should “unpack” the prominent phenomena. For example, the dependence of the discharge on pressure and pressure differences, ionization, and ozone production.

As is clearly explained by dr. Sahu, the electric arc (https://en.wikipedia.org/wiki/Electric_arc) is a less powerful phenomenon resembling lightning. It was originally studied because of its applications to lighting. The Duddell's arc generator was also deployed in telegraphy. Thus, there are also quite old books on that class of electrical phenomena, as that of Hertha Ayrton. They don't exhaust the topic.

Finally, Heinrich Hertz made use of sparks to detect electromagnetic waves. Sparks themselves don't yet meet any of the telecommunications transmission standards, but perhaps their interaction with matter can be modeled using a probability theory. One could study other aspects of that interaction using lasers.

"Above all, the accompanying luminous effects have none of the characteristics usually associated with electromagnetic waves, i.e. definite amplitude, frequency and phase."

But the luminous energy is visible and aren't visible light EM waves?

Thank you Sara madam, Sahu sir and Marcelo Perotoni sir for your replies!

Dear Suhas Dinesh,

you asked a difficult question. Perhaps my interpretation of luminous effects is less restrictive than yours. In my opinion the light detected by a linear receiver may “acquire” a code – for example a pass band – that it didn't have when produced by its source.

There is a very large current for a short time - this pulse radiates electromagnetic radiation. Hertz used smaller sparks to energise his spark-gap transmitter.  The lightning strike pulse generates electromagnetic radiation over a broad band, but not much at visible frequencies.  The heating of the air from the high current and the ionisation result in emission of visible radiation as atoms and ions return to their original low energy states.

A lightning spark generates a very broad-band signal - from DC to 10 MHz.  We are not allowed to use transmitters like that any more as they are very inefficient with their use of energy and bandwidth and interfere with everyone else.

Sara Liyuba

You are right - a receiver will "colour" the radiation it receives by the shape of the input filter.  Our eyes do this - using red, blue and green filters on different receivers, and radios and televisions do it too, allowing in only a very narrow part of the radio spectrum.