Clearly, water is important for the growth of mold. The mold grew best on bread sprinkled with sugar water because the sugar serves as food for the fungi. The more food that's available, the more fungi cells can grow. The mold also grew pretty well on the bread with plain tap water because the fungi could use the sugar and starch in the bread as food. The mold didn't grow as well on the bread sprinkled with lemon juice because lemon juice is acidic.
Acids hinder the growth of many common fungi and bacteria.