Could you leave a small patch unmown and repost a clearer picture of a full grown piece? It's hard to make out details.

Here is a closer view:

Much better picture. Thanks. Ranunculus looks right. Possibly repens but the leaves are almost all chopped off so we can't see enough whole typical ones.

Almost certainly creeping buttercup, Ranunculus repens. A very common weed in my area. It should be addressed by pretty much any broadleaved lawn weed killer but will return unless the conditions that encourage its growth - compacted soils, poor drainage, excess acidity and low fertility - are corrected.

I'm still dubious about its bring R repens. The leaves and habit don't look quite right to me. But it doesn't really matter as regards treatment.

I just treated it with a Roundup product for weeds in lawns. Says it will kill many things including buttercup. I also purchased Scotts Turf Builder with weed control. I did not spray it as container says to not spray within 48 hours of watering or expected rain and we are expecting rain within that timeframe.