OK, let's be fair to the OP. IS there any way to do this?
A multistep process that uses photo resists (like used today for electronics), where you would
1) apply a thin layer of goo/resin to, say, a copper sheet
2) expose the coated metal sheet to light
3) wash the unexposed 'goo' off, leaving only the light hardened/polymerized/whatever bits
4) etch the plate with acid
5) use that plate as a lithograph
Biggest single problem is to find that miraculous 'goo' with the necessary properties - sets under light, lets the unset bits get washed off, and resists acids.
Second problem is that grayscale might be really, really difficult. Resists do a LOT better with on/off, black/white.
Third problem may be that you need a printing technology that already uses lithographs before this of any use. But this is relatively minor.
Fourth problem - you need paper, good quality paper with repeatable ink absorbtion properties to make prints.
Would such a 'black and white (few to no greys)' 'photograph' be of any use? I doubt it. But as a 'toy' (like Hero's steam engine), it might be a thing to marvel at.