The device is essentially designed to trigger the shutter when sudden light variances are detected, but it leaves the metering entirely up to the camera, which is able to cope with the IR modification. I have never used a lightning trigger, nor do I know anyone who has used an IR camera to capture lightning (though I often imagined it would be able to create some stunning images under those conditions), so I can only speculate as to how that combination will work.
The 665nm filter would have been my recommendation for you (even though I often recommend the 715nm) because it allows for some visible light to pass through the filter. This should allow the camera to capture lightning better since it usually involves low light shooting.
Lightning does encompass the Infrared Spectrum so it should show up in the pictures fine with the 665nm filtration.