The weed you are trying to rid your lawn of is pennywort (Hydrocotyle americana, sometimes also known as dollarweed.  It spreads by seed and by underground rhizomes and is a perennial that blooms early. It thrives in moist areas.

The best way to control this broadleaf weed is to maintain a healthy lawn by regularly mowing at the recommended height for your variety of grass and watering deeply and infrequently to encourage deeper root growth.  Monitor your lawn for areas that may need improved soil drainage.   Fertilize your lawn appropriately; as recommended for your type of grass.

Remove the weeds you presently have by hand pulling making sure to remove all roots. If your infestation is too broad to control by cultural methods, chemical control options are available.

Use a herbicide designed to target this specific type of weed.  Your local nursery operator can help you select the most effective application.

When using any chemical read the label thoroughly and follow the instructions provided regarding the proper use and disposal

Thank you for your question.