This plant has taken over almost half my lawn. It seems to blanket entire sections of my yard. Any help identifying it would be greatly appreciated.
Two to compare with are Sedum acre and S. album. Once you find out what it is you can see if any suitable control options are being suggested.
This is certainly not Sedum album but it is very probably mossy stonecrop (Sedum acre), see e. g. http://www.omafra.gov.on.ca/english/crops/facts/ontweeds/mossy_stonecrop.htm.