Lavender (Lavendula spp.) is a lovely addition to a garden, providing fragrance and color in U.S. Department of Agriculture hardiness zones 5 through 10; however, it does require a little maintenance. Stray runners often make their way to unwanted places such as the lawn if you don't snip them back. Once in the lawn, the simple act of mowing encourages the spread of the plant.
Dig as many of the lavender runners out of the lawn as you can locate. After all, lavender may be unwanted in the yard, but that doesn't mean it isn't useful. You can use it fresh or dried in cuisine, sachets, soaps and aromatherapy essential oils. Remove the runners by scooping below the surface of the soil so that you capture as many stolons as possible. The stolons grow from the runners and are where new growth is initiated.
Spray glyphosate in an area of the lawn that is completely covered in lavender. Remove as much as you want before hand, and then spray the chemical to kill the rest. Apply only in areas where you don't care about any of the vegetation, because glyphosate is not a selective herbicide. However, if the lavender has completely taken over a section of yard, you don't have anything to lose. Wait a week before replanting grass seed, so the chemicals dissipate.
Overwater your lawn to prevent lavender growth. Lavender is tolerant to drought, and as a result does not grow well in overly wet conditions. This will help take care of any runners you missed as well as any new growth from stolons you missed.
Remove any new runners that sprout up in the same manner until you completely take back your lawn.