Try this: 2 cups of 3% bleach mixed with 4 table spoons of Dawn, (dish washing liquid) and very important, and 1 tablespoon full of any type of color that will show up n your lawn, add to 30+ gallons of water, use this equation: 1/2 gallon per 10' x 10' to a maximum of not more than this amount for an area of or equiv. to 100 sq. ft.
The bleach will do the trick but when mixed with the dawn and the color, the soap will stick to grass best and vines less, kill the grass by applying the mixture over the areas you want gone, in the early morning hours, it will deny the sunlight that the plant will need to starve off the bleach attack.
You will notice the amount of death and decay of that lawn within 6 days, you may have to apply the mixture a few times as you will want to kill the roots as well, that way it will be quite a while for the plant to come back and re-establish itself again.