"Your neighbor’s weed problems are YOUR weed problems. This trampweed (Facelis retusa) spreads by windblown seeds. This means that if your neighbor’s lawn looks like this picture, chances are your lawn could look like this next year. Working with your neighbors to address lawn problems can be a great community builder, and can create a beautiful neighborhood."
The Trampweed she refers to is pictured below.
UGA Extension Agent Frank Watson, in the FACES article "Weed Covers Turfgrass with Snowy Appearance," points out that seeds of Trampweed germinate in the fall and early winter, which means that May and June are not the months for trying to treat the lawn for this weed. Right now, this annual weed is producing its seeds and dying.
However, Watson does suggest some other tasks that might be done - beginning now - to reduce the weed's success in following years: "... since this weed is found on droughty sites with low fertility, make an effort to improve the turfgrass density by applying lime, fertilizer or increasing irrigation."
For appropriate chemical controls and the best timing for their use, contact your county Extension office.