Iron in various forms can be introduced to the lawn for two reasons: to correct soil deficiencies which might be putting undue metabolic strain on the lawn, and to get a deeper blue-green tinge out of the grass. Excess iron is what gives the distinct tint to Kentucky Blue Grass, and is a viable alternative to nitrogen-rich fertilizers introduced in early spring. Nitrogen generates a richer green, but can induce unwanted growth, hence the use of iron for aesthetic purposes.
Chelated iron or iron chelate is iron which has been treated with a chelating agent, ethylenediaminetetraacetate to be specific. This agent makes iron water soluble by rendering the iron ions inert and unable to react with other elements to form iron compounds. It comes as a brown powder which is spread across the lawn and then watered. It dissolves in the water and is quickly absorbed by grass. It's also very quickly used up, meaning multiple treatments over the course of a week are required. This combined with the fact that chelated iron is twice as expensive as iron sulfate means it's not used often.
Iron sulfate is also known as ferrous sulfate. It's made by dissolving iron shavings in sulfuric acid. As steel rods are passed through sulfuric acid in the process of making steel plating, iron sulfate is a byproduct of the steel plating industry. It is cheap and comes as a red crystalline substance which dissolves quickly but is absorbed slowly by the lawn. This is helpful as this type of iron treatment is needed less often. The downside is that it stains stone and any other substance it touches red. Also, repeated uses can cause a buildup of sulfur in the soil which can eventually reach levels toxic to the lawn.
Organic Iron Lawn Treatments
Technically, because iron is a mineral it cannot be considered an organic substance in the truest sense of the term. However, iron can be processed through non-chemically induced means, making it both safer for the environment and less likely to do harm to anything that should ingest it. Fertilizer which comes through fecal matter that's naturally processed by microbial agents contains a greater concentration of trace metals, iron the foremost amongst them.
The most well known of these organic iron lawn treatments is Milorganite, an all-purpose lawn fertilizer with a higher-than-average iron content. It won't burn the lawn, nor will it sink into the groundwater, but an iron treatment requires a great deal of this type of fertilizer which can smell very bad and takes weeks before it breaks down entirely into the soil.