Before I back myself into another corner, perhaps someone can advise me on the proper way to edit these chain links so that they come out like the second picture?
Is it even possible with just boolean operations?
First, ‘Group’ the sets. The outer, “laying flat” chain as one grouped set and then the inner, “standing upright” chain as another grouped set. You can then use the ‘Boolean Assistant’.
If willing, share this LightBurn file, and we can share back some workflow options. 
I really don’t think that works. It comes close. I did manage to get it done a slightly different way. I’ll try to explain… after “backing up” the layer to another, using subtraction, I created the three inner shapes you see in the link. Then made a union of the outermost pieces and deleted the remaining inner except what you see. Then I did a circular array of the three inner shapes previously created.
Voila!
Here’s a file for you to play with if you so desire:
chain-circle.lbrn2 (107.7 KB)
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Ah yes, I see it now - it is a bit more complex than from first glance, requiring more steps than I suggested. I give it a play. Thank you.
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