The best way to kill any weed in your lawn you can not easily pull is to choke it out with good/new grass. aerate the soil either by renting an aerator or you can simply get some of those
shoes that have 3in spikes. Yeah they look goofy and you look like a dork but just use them when you mow and it will help. Then get some GOOD, high quality seed (cheap seeds have weeds) and reseed or over seed your lawn. Put either a thin coat of good top soil (1/2") or peat-moss to help the new seeds to germinate.

