I apply Milorganite which supplies iron. Funny smell for a couple days, but not bad. The other things I apply to my lawn are coffee grounds and leaves, but I do not know if there is much iron in those. Mow high and if drought water deeply weekly. Did you do a soil test that said there was iron deficiency?

One thing to determine is what is causing the iron deficiency. Iron deficiency can be caused by a lack of iron in the soil, but it can also happen when there is plenty of iron, but the iron is in a form that is not readily available to the plants (usually due to the pH being out of whack).

Do you know why yor lawn is iron deficient?

Cool temperatures make the iron much less available to plants. Your soil may actually have ample iron, but it won't be released for plant uptake.

I agree with BP and Dori. It's unusual for there to be an Fe deficiency because soil Fe is inadequate. Fe is generally deficient because high pH causes Fe to form insoluble compounds with other elements, or because other elements are found at very high levels in the soil and are creating an antagonistic deficiency (P or Mn are the prime antagonistic offenders).

You can take steps to lower soil pH by adding organic matter or by using other pH lowering elements/compounds (FeSO4 is one, but be careful - it can cause an antagonistic Mn deficiency), or you can apply some form of chelated Fe with Mn, which is less affected by soil pH.

What makes you think you're dealing with an Fe deficiency?

Al

Iron deficiency in plants can occur in soils with ample levels of iron because the soils pH is not where it should be, where there is too much Phosphorus in the soil, where there is too much Zinc in the soil, or if there is too much Copper in the soil. A good reliable soil test is the best way to determine why that might be.
Chlorosis in plants has many causes, not just an iron deficiency. Pouring "something" on your soil to correct a perceived problem can create even more problems.

Where do you live? And why do you think your lawn is short of iron?