Where in the world are you? Bermuda says the southern tier somewhere.

What did a good reliable soil test say about the soil? What is the soil pH and nutrient level? Often a good healthy stand of turf grass will eliminate many "weeds" (unwanted plant) without the use of harmful, and environmentally destructive, plant poisons.

It could be some sort of Cudweed, Gnaphalium or Pseudognaphalium. Often found on poor or sandy soils. You might get a better id on the Name That Plant Forum. And clearer close up pictures would help. Also a location as kimmq mentioned.

I have these in my yard, they seem to be perennials. Amenable to being mowed, digging out the taproot is needed to remove. Mowing often enough so that new seeds are not formed/dropped will stop the spread of new plants, and this one does bloom again quickly after being mowed.

Your post does not include your location but your "lawn" looks similar to those in my area. The "weeds" provide better ground coverage than the vine-like grasses that constitute a lawn in this area like Bermuda, St. Augustine, torpedo, bahiagrass, centipede. If your interest lies merely in having some kind of soft greenery instead of bare ground on which to walk and play, there is no need to be concerned about the non-grass plants within the mowed areas.

There is a lawn forum here if it is your desire to try to cultivate a monoculture of grass.