This is Doveweed or another name given to it is Asian spiderwort. The scientific name is Murdannia nudiflora. It is an annual that can be controlled with a preemergent herbicide application done in early February. The only real other control option is to use Roundup at the high rate given on the label. I would also suggest to use a surfactant to help break up the waxy covering on the leaf.

Thanks much for the weed name.  Assuming that Doveweed dies in the winter, what pre-emergent product(s) do you recommend and at what rate?  I need to get rid of this stuff or I'll have no lawn.

There is a post emergent herbicide called Celsius. You will really only find it in landscaping supply stores or the web. It may take a couple of applications to see some good results this late in the summer. However it would be a good product to use next June after to see any doveweed that germinated from any seed that was produced this year.

As far as a pre- I would suggest Suflan, Balan, Halts or Bonus S.
 

I own Celcius and have used it to disappointing results.  Do you know the recommended strength for late season doveweed?

From what I have read, 3.7 oz/ac.