Luck and Rule Inversion

does the “Lucky Lightning” modifier affect all lightning damage, or does it simply roll lightning damage twice and take the higher value? Also, when paired with “Invert the Rules Support,” will the reversed probabilities result in better outcomes?

It should work with invert the rules. It will roll the damage range twice on lightning, take the higher value, then when it gets to the part of the damage calculation where resistance is calculated it will apply the invert the rules interaction.

Unsure what you mean by "all lightning damage". If you are talking about more or added as modifiers, they will be included.

Here's a description of how it works. See step 3.5 and 6.4. Doesn't describe the inversion, but should be part of calculating in 6.4.

https://www.poewiki.net/wiki/Receiving_damage