Quantum effects appear at the microscopic level, or at highly organized solids and fluids (superconductivity, superfluidity for example). This is due to the very small value of the Planck constant in the Heisenberg uncertainty, which is obeyed automatically macroscopically down to micron levels.
Lightning strikes follow classical electromagnetism and thermodynamics. It is potential differences and the phases of matter as energy is released and the air heated to high temperatures. Lightning has temperatures of plasma as discussed in the answer here .
There is an indeterminacy coming from the boundary conditions for the classical electromagnetic + thermodynamic solution, coming from the classical statistical mechanics of the ensemble of atoms on the way between the high potential of the cloud and the earth, but it is classical indeterminacy, not quantum.