Actually, let me walk that back a little - it can be done, it’s just slightly awkward. LightBurn will auto-snap new objects to nodes of an existing one, so, for example, you can create a circle exactly centered on any node.
Here are two random shapes, both with interior nodes I want to align to:
If I click the Circle tool, then hover over a node, you’ll see the cursor change, like this:
While dragging, press the Ctrl key to draw the circle “Center out”:
Once that circle is created, the center is the exact location of the node under it.
If you did that for both, then did the math to figure out their difference, you could use the equation support to apply that difference to the position of one of them in LightBurn. Not ideal, but possible.