Taller ht of cut, and higher rates of nitrogen may help. Thicker grass is more weed resistant.
Perhaps also suggest to customers to over seed or switch to a more dense premium Kentucky bluegrass.
Naturally allowing the lawn to become thin or develop bare patches allows dandelions to increase as the seed is carried on the wind. Remember dandelion seed takes hold in late summer or fall. The plant has to achieve about 4 months old, and 6 inches in diameter to be strong enough to put up a blossom by the following spring.
Its possible that the organic iron compounds applied in fall would kill the new young dandelions easily...the result...no dandelions in spring.
Meanwhile, hand out a receipe for dandelion wine and take heart...the yellow flowers are usually gone after two mowings.