What would happen if a castle was struck by lightning? How much damage would be done?

Assuming a classical, stone castle with towers... not much damage.

If the walls were wet from the rain, the water would flash into steam. Moss or vines growing up the walls might get burned off.

The stones and any mortar used in the walls would be of poor conductivity, but present a huge volume and mass, and might sink some current to ground, as well.

None at all if a lightning conductor was installed.

There would be minor damage to the crenelations, machicolations, and corbels.