If it is Black Medick (Medicago lupulina) then it is a big problem. Lawn specific weed killer may work in time. We spend ages going over the lawn pulling it out, making sure we get the roots as well.

If the flowers are tiny with a clover like leaf they could be Lesser Trefoil and it will spread.

With black medick, you may need to add a surfactant to the weed killer, or the spray will just bead up and roll off the leaves. Some brands of weed killer already have surfactant in them, but most do not. As usual, check the label.