Purslane Or Prostrate Spurge

This looks like purslane, a succulent annual that grows quickly from seeds. It especially flourishes in bare areas in the lawn. Since it is an annual your efforts at control should be the following: Dig all you see now to prevent them from going to seed in your lawn. Rake bare areas in the lawn, top-dress with a little loam or mix of loam and compost, and over-seed thickly with grass seed in April of next year. The thicker and healthier your grass, the fewer weeds you will have of all types. Have the pH of your lawn tested and lime only if needed. Next spring if you want to prevent this weed from germinating again you can use a pre-emergent herbicide according to directions. Ask at your local garden center for product recommendations.