You don’t stop with just killing or pulling the dandelions, crabgrass, or other weeds in your lawn. You are just leaving spaces for new weeds to occupy.
The trick is to wait two weeks and then either patch small areas or overseed the entire lawn with lots of new grass seed to fill the holes left by the dead weeds. You can do this job in the spring, but the fall is the best time to plant grass seed, and the weeds are still growing strong. Grass seed planted in the spring often struggles to survive the heat of summer while still in the seedling stage.
So it is best to kill the weeds in late August and in early September overseed the lawn; next year you will have only a few dandelions and such and those can be hand dug with little effort. In a very bad infestation, maybe you’ll have go to complete lawn renovation or have to overseed two years in a row to get the grass density you need to keep out lawn weeds forever. All the dandelion and crabgrass seeds in the neighborhood can land in your yard, but because there is no space in the soil and no light available at soil level, the seeds can’t germinate.