You may run into a couple of problems with a strobe:
First, they're usually pretty rhythmic and don't really look that much like lightning. If you're looking at a photographic strobe, you're liable to run into problem number 2...
...which is, the pulse of the strobe is so fast that you run the risk of it not registering on camera, especially if you're shooting 24p or 25p. If you're shooting interlaced, it will likely only register on one field, which is better than nothing, though, again, doesn't really look like lightning.
If you can rent an old carbon arc light with a manual adjustment, that'll produce a perfect lightning flash because that's exactly what it is. Or, for a cheaper alternative, find an arc welder who'll bring his gear to the set.