4-Way with no Neutral

There are two lights one on each side of the hallway.

Yes on testing the one white reads 120V all other wires are dead after removing the nut.

I assume the red is the traveler.

Oh and I can’t get up to the box up in the attic but I may be able to take the fixtures off.

After digging around I just found another white and black pair of wires nutted off as well.