I have read that lightning bolts have a difference of potential of 300 Mega Volts. Does it mean that the electrons in the cloud have an energy of 300MeV each? I found that astonishing since that energy is way bigger than the electron rest mass-energy, which is 0.511 MeV. Such big energy would allow quantum effects as pair production. Does this kind of effect happen on lightning bolts?
300 MV is accurate for the potential difference between charge centers. But possessing this potential energy doesn't get you any quantum effects on its own, the electron needs to accelerate through the E field. But the air between charge centers is both non conducting any has drag.
If you can overcome those obstacles, then you would indeed get electrons with energies in the MeV range. This phenomenon is known as a Terrestrial Gamma-ray Flash, and can produce e-/e+ pairs, free neutrons, etc