Lightning is brutal. That's a lot of current (and a just a little bit of voltage in a really short amount of time.
A strain gauge is working on tiny currents and really small voltages.
If you take a look at the spec sheet for the SNAP-AILC you can see that the module has an over range voltage of around 3.3 to 3.3 millivolts.
So typically its working at less than this when connected to a load cell.
Also note the other two main specs, the 'Maximum Surivable Input'; +/- 15 volts and 'Maximum Operating Common Mode Voltage' of 250volts.
This then I think is your answer to your second question, is lighting protection built into the module?
Air breaks down at around 33 kV per centimeter.... so we are well past our 15 volts with just a one centimeter spark.
So, I think the answer to your question is some quality time with Google.
You are looking for a protection device, sacrificial or other wise, that can pass a millivolt signal without attenuation, but block or bypass any voltage over +/- 15v.
Lets know what you find and if it works.
I'm sure many of our fellow forum folks would love to know what you find and your real world experience with said device.