I think that you may have a weed known as dichondra. This is an spreading ground cover that some people plant as an alternative to turf grass, but it can also be a weed.

There are both cultural and chemical approaches to control weeds in your lawn.

Cultural methods can help to keep weeds at a minimum, though sometimes these can be a challenge depending on your specific conditions. Mow your lawn at a taller height and avoid over-saturating your lawn with water as both dichondra and creeping Charlie like moist conditions. If possible, improve drainage. However, make sure your grass has adequate moisture for growth to maintain its health. Cutting management is also important. Letting your grass get a bit taller/longer will shade out weeds and make them less competitive.

For chemical control you can use a product labeled for turf that contains 2,4-D. Both these weeds are broadleaf weeds so the same products can be used to control them. Be sure to follow instructions. Depending on the type of turf grass you have, the rates for application are different as bentgrass, carpetgrass, centipedegrass, and St. Augustinegrass are more sensitive to the herbicide than other grasses. Spray when weeds are young and actively growing. It is best to use a low-pressure sprayer to avoid danger of injury to flowers and ornamentals by spray drift. Do not spray on windy day.

The following advice is from The NC State Turfgrass Pest Management Manual 201~rfPestManual (1).pdf : WEED MANAGEMENT PRACTICES Proper turf maintenance is also the key to perennial broadleaf weed control. Spray weeds with an appropriate postemergence herbicide in March or April depending upon your location. Select the herbicide according to the weeds to be controlled and the tolerance of the turfgrass. For example, bentgrass and hybrid bermudagrasses are less tolerant to 2,4-D than bluegrass, fescue, and common bermudagrass. Centipedegrass and St. Augustinegrass are also sensitive to products containing 2,4-D. When spraying centipedegrass or St. Augustinegrass, use products formulated for southern grasses as they contain reduced amounts of 2,4-D. You may need a product containing two or three broadleaf herbicides if several different weeds are present. Some perennial broadleaf weeds may require a second herbicide application four to six weeks after the first application.

Once you have the weeds under control, consider using a pre-emergent herbicide to prevent new weeds from establishing.

For more on weed identification you may wish to view this website supported by NC Extension: https://www.turffiles.ncsu.edu/weeds-in-turf/

For more information and a description of dichondra see: https://content.ces.ncsu.edu/dichondra