Deleted

Are the lamps in parallel ?

May you draw the exact schematic? (or repost a link, if you have already published it)...

All i can see here is minor dependance between the lamps by sharing the preheat current on their neutral-side electrodes. But i seen somewhat similar situations in miswired ordiunary 2x36w fixtures (both lamps with neutral on the same side, and starter wires crossed between tem) and as long as both lamps are intact those fixtures dont have a problem to strike both lamps

I was thinking that too since a simple preheat circuit has been complexified many times...LOL.

Just to have a clue, what did you do there - as you said, there are endless possibilities...