Many years ago when I was a 'lecky, I worked on a very expensive lathe light fitting that was using fluorescent tubes.
I was amazed that a lathe actually had a fluorescent fitting because of strobe concerns but I found that the manufacturer "cheated" a bit for safety reasons.
Fluorescent light fittings In most commercial use locations have power factor correction capacitors fitted directly across the connection terminals otherwise the power metering will not be correct & there can be circulating current problems.
The manufacturer of the lathe fluorescent light fitting used a dual fluorescent light fitting with two separate ballasts & only had a power factor correction capacitor fitted to the one one fluorescent light.
The power factor correction capacitor caused a phase shift on the one lamp compared to the other.
I actually ran the fitting with no power factor correction capacitors fitted at all & with the one fitted & when the one capacitor was fitted then the strobe effect was not visible.
I suppose that it may be possible to phase shift some LED lamps as well with a capacitor if they use an actual iron transformer for the power supply so you could have dual LED lamps set up in a similar way.
Regards,
Brian.