Q. how to control wild strawberry growing in lawn
Controlling Wild Strawberry in your lawn:
Of course don't confuse this little runner with ediblewild strawberries. There are several different kinds of those wonderful little plants ('wood strawberries' have runners; 'alpine strawberries' are clumping plants), and all are delicious. After being discovered growing wild in European woodlands centuries ago, they were quickly transplanted into gardens.
There's not a lot of surface area on this plant, so herbicides of any kind are going to be useless, plus not safe for the environment; there's just nothing for them to land on. That makes physical removal the answer. The weed's habit is to run across the ground until it finds a spot it likes and then send down a root system, from which more vines run; and as most of our lawn owners acknowledge, it is extremely easy to pull out of wet soil.
Before you attack it, however, do a little work to prevent new infestations. Surround the outskirts of the areas you want to keep 'strawberry-free' with deep edging. Leave two inches of the material above ground to prevent the weed from walking overtop it, and keep an eye on this Maginot line throughout the season.
Then mark off sections of the infested lawn and work small areas at a time; don't try and conquer this Rome in one day or you'll wind up cutting corners and have to do it all over again. Have a hose or watering can at the ready and feel your way along the vine until you get to a rooted section. Soak that area well with water, and then pull slooowwwlllyy and gently. You should see the tiniest of root hairs still attached when that big root comes up. Trash the collected vines; don't compost them.
Then, when you're theoretically finished, keep that lawn thick, strong and free of the bare spots that offer weedy opportunity. Overseed fescues and other clumping grasses at least every other year to compensate for their lack of lateral growth. (Overseed warm season lawns in the Spring; and in the Fall.) Then never cut your lawn lower than the recommend height (a minimum of three inches for cool-season lawns), and this weed should forever be stuck on the outside looking in.
Hope this is helpful.