Voltage is a measurement of Electro-potential.
Let's take an example: a tall bucket full of water has a hole on the bottom. The Voltage is like the height of water, and the electric current is like the size of the hole. Higher the water level from the hole, faster the water flow, and larger the hole, more water flows and empties the bucket. Likewise, more current you draw from a battery, faster it drains out.
Higher voltage means the lightening can pass though a longer distance through the space, and thetrefor increase the possibility/frequenct of lightening.
The size of clouds makes the lightening more "stronger". Larger clouds have more electrons, but the electron "density" difference makes the voltage.