Prostrate Knotweed prefers compacted soils. It can be difficult to control but you do have options.

You will have to look closely at your lawn. With our warm spring it may be too late for a pre-emergent this year. 

Go for a post emergent when the plants are just past the seedling stage. You may have to repeat for larger plants. 

When you are looking at products, READ THE LABEL. 

Be sure you purchase a product that is safe for use on lawns. 

Be sure that it states on the label that it is effective on Prostrate Knotweed.

Follow all safety instructions and do not use on a windy day or if the temps are above 80°.

More is not better, less is often ineffective so measure your dose.

Since knotweed likes compacted soils, you should probably have your lawn aerated in the fall. 

Postemergence (Lawns)

• 4) Selective - Postemergence (Lawns)

  Selective, postemergence broadleaf herbicides can be used to control these weeds in lawns. Commonly available homeowner products contain one or more of the following active ingredients: 2,4-D, 2,4-DP, MCPP, MCPA, dicamba, triclopyr, carfentrazone, sulfentrazone, quinclorac. Make sure that the products being used state on the product label that they are for lawn use.

https://apps.extension.umn.edu/garden/diagnose/weed/broadleaf/creeping/pknotweed.html