I can't identify the weeds as the picture is blurry when I blow it up. The first step in rehabing a lawn is to know which weeds are a problem. Once you know that, you can find information on this website on how to control it. After weed control, you'll need to reseed the lawn this fall as there will be bare patches which will "sponsor" a new set of weeds. If you are adverse to using herbicides, your best option is to kill everything and start over with seed or sod. I've provided three links. One goes to lawn weed ID and one on killing the lawn without herbicides. The last one goes to a listing of all the lawn articles on this website.
Could you restate your question? Your link is broken.