But I mean, if you're seeing the strobing of lights at your site, I wouldn't think it was because you accidentally miswired AC the same way. If on purpose, you would have already told them how to fix it.
If related to the type of lights used, are you and customer using LED? Have you tried incandescent?
For a light to completely turn off, then on, either suggests voltage drops to near zero (time scale of a second in the video), or to the point of causing electronic ballast to turn off. Might have a turn-on delay.
Or, electronic control signals (including inadvertent response to interference.)
I was recently at an EMC lab with equipment being tested. Injection of 10Vrms RF on top of AC caused a PDU (controllable power strip) to switch AC on and off, blowing up power supply in another box. It was certified to 3V lab environment, but not 10V industrial.
If you haven't seen anything wrong with the waveform, go back and look again.
It is almost certainly bad, either viewed over a longer timescale to capture the dropouts, or a shorter timescale to see high frequencies.
Between time domain and frequency domain displays, it should become clear. I hadn't thought scope could do it, but an 8 bit scope can clearly resolve -70 dB peaks (down 1000:1 below fundamental). Signals below ADC resolution and below noise floor, which are repetitive, can be seen with FFT.