Good question - it is not currently known how thunderstorms generate the electric charge separation necessary to power lightning strikes, but obviously they do it, while ordinary wind clearly does not. A clue comes from the fact that volcanoes also often generate lightning, so I suspect that it has something to do with the contact between gas, liquid, and solid, all interacting.

Lightning needs static electricity, because lightning is the huge spark that happens when electrons get back together with positively charged things and neutralize the charge.

There's not enough static electricity when it's windy to make lightning.