With any weed-service contract, you have to expect that the chemical used might not kill ALL species of the weeds you have. It would be better for you to do some research into the particular weed--see what is effective on it.

When a liquid broadleafed weed killer is used, it is recommended to water the area first....water it rather well, then wait for an hour.
This acts as a capilliary action to draw the weed killer down to the roots of the weeds. Often, in warm areas, weed killers are used on nice, windless days, during the hottest part of the day and a lot of the liquid evaporates or runs away from where you want it.
The watering first can help defeat that.

Dependent on what kind of grass will stand up to broadleafed weeds might be another thing to look at.
Generally, if you have tough weeds, then a second application is warranted. But, do give the first application a chance to work. Overkill will only hurt your soil and its ability to grow grass.

If your grass, what grass you do have, is poor, that suggests your soil is not up to scratch. Whether you dig in organic matter or just layer it over the surface is up to you. But, if you can see your way to putting a layer ...1/2" - 1" of compost or good topsoil, over the area lawn in spring and fall....and do that for the next four years minimum, this will often result in much improved lawn.
I realize in your neck of the woods, being a transitional state---through middle America, you might use a number of types of grass. What you have to do is find a type expressly for your circumstances....and stick with it.
In the north, we regularly use a combination seed...Kentucky Blue...for sun; perennial ryegrass for toughness--able to take heavy traffic, and fescue for where shade might come on it. The independent grasses don't take on their own color or growth, they swim together and makes for a nice lawn.
In your area, such combo wouldn't work....it would burn the first time your Oklahoma summer hit it.
But, a combination of grasses you do use, might work.

What do your neighbors use....what success does your neighbors have with lawns and does the local full-service garden nurseries give any advice.

You might go to your local state funded university EXTENSION SERVICE, provided by such institutions.
Thus, Oklahoma State and other colleges are at your beckon call. They have agriculture departments and many do soil tests at nominal charge, or free of charge. After all, they are funded by you....the Oklahoma taxpayer.
A phone call might tell you if, and how to go about submitting a soil test.
(actually its 'soil tests'....they require multiple samples from different parts of your property to give an accurate up-to-date result.

>"When a liquid broadleafed weed killer is used, it is recommended to water the area first....water it rather well, then wait for an hour.
This acts as a capilliary action to draw the weed killer down to the roots of the weeds."

Jeannie:

Where do you come up with these things? Cite your references, PLEASE!

Common broad leaf herbicides are systemic and absorbed by foliar parts of a plant and are then translocated within the plant system to tissues that may be remote from the point of application. The herbicide itself is absorbed via leaf tissue area, not roots. Your procedure is an old wife's tale - nothing more ... and I have references. DO you?

To OP:

What exactly is you question? (in a shorter form)