Sugar is more of a herbicide. Grass fertilizer is nitrogen. Sugar has no (as in ZERO) nitrogen. It's carbon. I guess to the extent sugar kills weeds, and to the extent weeds aren't around competing for nutrients, it might help lawn grass, but sugar sure doesn't help lawn grass directly. If anything, sugar decomposition uses soil nitrogen, which certainly won't help lawn grass.

Sugar doesn't cost a lot less than high nitrogen lawn fertilizer. If you're going to spend money on your lawn, spend it on a bag of high nitrogen fertilizer instead of a bag of sugar.

The sugar isn't feeding the lawn as much as it's feeding microbes in the soil. More microbes means more nutrients available to the lawn. More often people use horticultural molasses, which is also high in potassium, calcium, iron, magnesium and other micro nutrients. You should be able to find it at plant nurseries. It's usually in liquid form, but may be had in a flake/granular form as well.

That's true, but with regards to nitrates, ammonium and potassium nitrate are VASTLY more nutritious than anything that soil microbes could release.

And then ...

https://gardenprofessors.com/molasses-malarkey/