Grows all year long in Berkeley County lawn which was previously a pasture. Roundup and Scott’s does not kill it.
the plant in this picture is a Rubus, very likely the dewberry, Rubus trivialis. It is hard to be 100 % sure with this image.
You also sent another image of a different plant that seems to be an Aster sp. of some kind, or less likely, a goldenrod. It is hard to identify with only the rosettes.
Roundup should be able to kill both of these. It takes a few days after application. Both are native species.
Steve Hill, Ph.D., Botanist, SCNPS