How do I get rid of the Blackseed Plantain & Buckhorn Plantain weeds that have taken over my lawn?

The weed killer products work but you usually need more than one application. So on the one side of your yard where they just look wilted you need to re-apply the weed killer. You can used the hose attached type and not just the spray bottle type. Make sure you buy the type that meters itself so you don't have a problem again with it being too strong. Now for the area of your lawn that you burned. Thats probably what happened its just burned and it will recover. If it does not recover then you will have to reseed or put down new sod. To reseed just rake up the old dead material down to bare dirt then broadcast some new seed. Take some straw or peatmoss or gr clippings and cover the new seed with it. That will help keep it moist until it germinates and you need to water it and keep it moist until it germinates. That takes from 3 days to 2 weeks depending on the variety of gr seed you use.