Bedstraw or cleavers (Galium species) is a low growing weedy weed with a small white flower in the shape of a cross, together with small leaves that grow in whorls, which are bunches of leaves (6-8 in this case) growing from the same place on the stem. I won't try to guess at the species, for that we would need more detail from a single plant, so if you can try teasing a single stem from root to tip - if it is bedstraw then that will be a hard task that will take you more than a few minutes; check the root, which may be a rhizome. As you can see from your picture the grasses and bedstraw become very matted so it is hard to pick out the relevant details.
Once established it is hard to eliminate without replacing the lawn. Dealing with it is quite a chore so see if you can live with it first, walk on it, mow it, rake it and so on and if it is manageable then you save many headaches. Since it is not a grass it may respond to broad leaf weed killers but as you can see the leaves are not very broad.