Question
If you put the sugar on the lawn to enrich the soil, won't that bring ants?

Answer
Not only ants but bees and other insects. Sugar is applied to provide a nutrient solution for beneficial bacteria to inhabit the soil. The bacteria cannot handle solid food so I would  lightly water in the sugar so that it gets down in the soil and be assimilated rapidly. I have no "hands on" experience of sugar applications but I have a pretty good idea of how soils and organisms interact.