The plant in this picture is probably mossy stonecrop, which is also commonly referred to as Sedum.  There is no easy fix for this particular problem.  A long term strategy would be to build up organic matter in the soil by mulching leaves into the lawn for several years. The sedum thrives in dry, nutrient poor, sandy soil, which is why it is outcompeting the turfgrass in the lawn. A soil test will tell you what nutrients the soil may be in deficient in. Then, if you can develop the soil so that it holds more moisture and nutrients this will tip the scales back in favor of the turfgrass and it may be able to push the sedum out. Sedum really doesn’t like moisture, so a little extra watering wouldn’t hurt either. Of course, bear in mind that sandy soil will not hold much water, so if you irrigate excessively in sandy soil you will just be wasting water and washing nutrients away. This MSUE article offers some chemical control options: http://msue.anr.msu.edu/news/scouting_for_weeds_mossy_stonecrop