What is the name of this weed? How do you get rid of it without damaging the adjacent lawn?

The weed has reddish stems, 1/2 inch oval leaves with a shorter reddish-purple linear line in the center, The plant lies flat to the ground, turns reddish orange as the ground gets too dry. The limbs/stems extend fan-like up to ten inches from the central root.

What is the name of this weed? How do you get rid of it without damaging the adjacent lawn?
It sounds like spotted spurge (chamaesyce maculata). You can spray with Roundup,(glyphosate) but overspray will probably burn the neighbor's turf. If you prefer an organic spray, you can mix 1 gallon full-strength 10% vinegar,2 oz. orange oil, and 1 cup liquid molasses. Overspray from this mixture can burn or kill other plants and grasses as well. About the only way to get rid of this noxious weed, with 100% assurance of no chance of harming the neighbors grass, is to hand pull it. Home Depot has a tool called "Weed-Hound" that allows you to pull weeds like this without bending over. It works best on plants that form a rosette and lie flat on the ground. You can probably find it in the garden dept. of any of the "box" stores. I paid $20.00 at HD.
Reply:Aussie said Ortho-weed-be-gone and is likely correct. Because the weed has oval leaves, it is likely considered a broad leaf weed. Weed Be Gone kills "broad leafs", that is why Weed Be Gone is generally safe on turf grasses- grass is not a broad leaf.
Reply:M60
Reply:ortho weed begone
Reply:pull some and head to your local nursery.