I want to cut a horizontally and vertically aligned grid, similar to what tables use. This is very sparse, so a flood fill seems the only reasonable option. But the movement pattern still feels stupid, e.g. for the thin vertical lines LightBurn will still process them horizontally, adding lots and lots of back and forth movement. I guess that traversing the thin lines in multiple vertical passes would result in less overall movement as well. Can anyone comment on that intuition and whether I can trick LightBurn into doing that without having to split up the grid into different colors to force separate horizontal and vertical components?
The notion of “filled” shapes is intended to produce a uniform result over a region, so using it to create thin lines is something of a corner case.
If it’s a simple rectangular grid, this is trivially easy.
Create two Fill layers with identical speed / power values, with one scanning vertically and the other scanning horizontally.
Draw a single vertical rectangle of the grid’s height over on the left side and assign it to the “scan vertically” layer. Use the Array tool to duplicate it across the grid’s width.
Draw a single horizontal rectangle of the grid’s width along the bottom end of those vertical rectangles and assign it to the “scan horizontally” layer. Use the Array tool to duplicate it along the grid’s height.
Fire. The. Laser.
Also, if cutting the lines as single vectors, rather than as filled rectangles, would produce a good-enough result, that will go even faster.
Set up a layer with the proper Line speed / power.
Do the grid thing again, with lines rather than skinny rectangles, and assign both directions to the same layer.
Fire. The. Laser.
Done! 
Of course, I’m sure I misunderstand some of the complexities, but maybe that’ll give you some ideas.
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