I personally don't grow Lithops, but it seems to me just water limescale deposit,

I agree with Roger. Have you been misting them? Try and use rainwater intead if possible

I have not misted them, but I can. I can't collect rainwater (apartment living) but I could use distilled water. I have done some reading today about using white vinegar and distilled water to dab the white spots with it. Thank you both for your replies. :)

I wonder if it has to do with splitting.

I don't believe it has anything to do with splitting, looks very much like water marks. Or it could be salts from too much fertilizer - I don't think OP uses it on Lithops?...

Never seen that on splitting Lithops. Since Jan hasn't had them long, I think it might just be old watermarks from when they were being grown elsewhere

I did add some succulent plant food - maybe the residue is from that?

Very possible, especially if you sprayed it on

It was a pump spray; I sprayed it into the soil.

I have very few and am no expert - but do they really need fertilizer? Maybe once -twice a year, but IMO, fertilizing newly repotted plants may be too fast. It may be better for plants to be established before giving them ferts - correct me if not right.

The splitting is how they reproduce:)