According to the Lightning Strikes website, All Lightning Strikes fixtures "limit the shortest flash duration to 1/24th of a second." Lightning Strikes can be synced to the camera shutter, but only when using the "16 Light Sequencer."
Then there is the Unilux strobe system, which flashes "in sync with the camera shutter, exposing each frame for 1/100,000 of a second." As far as I can see this exposure time is not adjustable.
Finally, there is the AF1000 DataFlash, and similarly designed competitors. Minimum flash duration is either 1/120 of a second, in the case of 60 Hz power, or 1/100 of a second in the case of 50 Hz power, and is adjustable in multiples of this basic rate. This is the unit one would expect to encounter in a theatrical setting. There is no obvious way to sync it to the shutter.
Perhaps it would be possible to sync Lightning Strikes and AF1000 DataFlash units by converting the camera shutter sync output to MIDI and then inputting the MIDI control signal to a DMX control board. But I have never seen it done, and can only speculate that it might be possible.