Lawn invasive grass and ground vine
Left photo - this looks like ground ivy, a perennial broadleaf weed. Here is our page on management in a lawn. If you do not want to use an herbicide, you can handpull or use a weeding tool to remove in moist soils. https://extension.umd.edu/hgic/topics/ground-ivy
Right photo - looks like nimblewill, a perennial warm season grass. Here is our page on management in a lawn. If you do not want to use an herbicide, dig it out. It has a shallow root system but will regrow from any pieces of the root left in the ground.
Reseed the areas to maintain healthy, dense turf that can compete and prevent weed establishment. https://extension.umd.edu/hgic/topics/seedingsodding-lawns