Is there a particular reason why you’re going through a 3-stage process?
LB can load DXF format which Inventor should be able to export to directly. That will probably be the best path to avoiding artifacts.
In this particular case I suggest you identify the first step in the conversion where the paths are lost. I suspect the AI file and SVG files already have unclosed paths even before coming into LightBurn.
I wrote a fairly lengthy post about the various tools and strategies for closing paths that might be worth a read.
As @jkwilborn has pointed out, though, if you have extraneous line segments those will need to be addressed before trying to join the segments.