Lime, in the sense of applying it to a lawn, is either pulverized or granulated limestone. The main component is calcium carbonate. Lime with a high calcium content is referred to as calcitic lime and has the added benefit of adding calcium to the soil. Some limestone contains a significant amount of magnesium and is referred to as dolomitic lime. Dolomitic lime adds magnesium to the soil and could be used if soil tests indicate a magnesium deficiency.
Pulverized lime is powdery and messy to apply, often causing lime dust to blow everywhere that is why the Green Lawn Sprinkler Company uses only granulated lime which dissolves with subsequent rains or irrigation.
You may need to add lime to your soil if a soil test indicates a pH level below the optimum of 6.0 or 7.0. Soil pH is a measure of a soils alkalinity or acidity. A soil is acidic, or "sour", if it has a pH below 7.0 (neutral). Soils can be naturally acidic but can also be acidified over time by natural leaching, the use of some nitrogen based fertilizers, excessive rainfall or irrigation, and acidic water sources. A pH below 6.0 causes important plant growth nutrients to become "bound up" in the soil making them unavailable to the plant. As a result, the turf can decline including a loss of color, reduced vigor and diminished ability to recover from heat and drought stress.