It may be easier to till up the lawn and start over instead of trying to treat for the unwanted plants growing there.

I would have a good reliable soil test done first so I could make necessary adjustments for soil pH and major nutrients as well as getting adequate amounts of organic material into that soil.

Some other simple soil tests that could be of some help are,

1) Soil test for organic
material. From that soil sample put enough of the rest to make a 4 inch level in
a clear 1 quart jar, with a tight fitting lid. Fill that jar with water and
replace the lid, tightly. Shake the jar vigorously and then let it stand for 24
hours. Your soil will settle out according to soil particle size and weight.
For example, a good loam will have about 1-3/4 inch (about 45%) of sand on the
bottom. about 1 inch (about 25%) of silt next, about 1 inch (25%) of clay above
that, and about 1/4 inch (about 5%) of organic matter on the top.

2) Drainage. Dig a hole
1 foot square and 1 foot deep and fill that with water. After that water drains
away refill the hole with more water and time how long it takes that to drain
away. Anything less than 2 hours and your soil drains’ too quickly and needs
more organic matter to slow that drainage down. Anything over 6 hours and the
soil drains too slowly and needs lots of organic matter to speed it up.

3) Tilth. Take a handful
of your slightly damp soil and squeeze it tightly. When the pressure is
released the soil should hold together in that clump, but when poked with a
finger that clump should fall apart.

4) Smell. What does your
soil smell like? A pleasant, rich earthy odor? Putrid, offensive, repugnant
odor? The more organic matter in your soil the more active the soil bacteria
will be and the nicer your soil will smell, to a point. Too much organic matter
can be bad as well.

5) Life. How many
earthworms per shovel full were there? 5 or more indicates a pretty healthy soil. Fewer than 5,
according to the Natural Resources Conservation Service, indicates a soil that
is not healthy.

kimmq is kimmsr