Modeling a transient signal of Lightning?

Is there any reference telling the detail of how to model a lightning as a electromagnetic pulse (EMP)? Is it a Gaussian beam in space and Gaussian signal in time domain? Or something else?

Try to google EMC compatibility testing. There are international standards on high-voltage pulse testing of components and systems.
There are some recent studies on lightning, still not giving too deep understanding of the process. I am afraid that your questions remain unanswered.

The fast di/dt (rise time) will approximate a dirac function with a wide band frequency response (or Gaussian noise)