Spurge Weed Problem in Lawn Controlled with Fertilizer, Irrigation and Mowing Height

Q. We have a weed problem in our back lawn and I think it is called spurge. The leaves are small and it's kind of viney. When I pull it, I see this white sap coming from the broken vines. I can dig it out of the soil where I have gazanias but cannot do the lawn that way. Any advice would be so welcome.