selective infill  

RE: selective infill

You don't want to have infill in the areas where the picture is located, just perimeters. Set the number of perimeters high enough so that no infill will be used in the image area. Shadows of infill patterns would be visible and ruin your image. Make the background area thin enough for a stable print then enough light will pass through. At least those are the settings that I used for printing lithophanes.

RE: selective infill

What orientation are you printing your lithophane? I usually printed lithophanes standing up on edge to get higher resolution for the lithophane thickness than layers will if printed flat. (But maybe you are going for a posterized effect.)

I did my lithophanes similar to how @walter-layher describes with more perimeters than will fit to force the entire thickness to be solid without any potential bubble voids that a 100% infill might cause. Another tip that you haven't asked for: If you are printing on a bed slinger, when printing lithophanes standing up on their edge (or any slab-like print), orient it so the width is parallel to movement of the bed. This will reduce the amount of motion induced wobble in the print as you get towards the top.

RE: selective infill

Yes I'm printing vertically as well.  I was really surprised to see that they didn't fall over.  I appreciate the thought about the orientation of the print.  I was actually doing it 90deg off.  So the bed was moving more than the hotend was.  Doing it the way you are suggesting the bed is going to move a lot but it will be parallel with the long axis of the print.  But without any infill now, just drawing circles, will it really make much of a difference?  

RE:

To be honest, I haven't tried printing with the long axis 90 degrees from the bed movement. But the example I used to formulate my reasoning is if you have a ruler (or similarly shaped rigid object), hold it up vertically. Pinch the bottom edge across the short dimension and wiggle your hand back and forth and try to keep the ruler from wobbling. Then pinch the bottom edge across the long dimension and repeat the movement. It is much easier to keep the ruler from wobbling when pinching across the long dimension.

Through the lithophane when made with all perimeters, there will be portions where there are partial perimeters. Islands of thick portions with thin portions on either side. You'll get a lot of jerky motion from travel moves between these thicker islands. I would imagine that Input Shaping should be able to mitigate a lot of the wobbling though. I haven't printed a lithophane in quite a while, and when I did it wasn't on a printer that had IS. So maybe my orientation advise is outdated.