There are lots of ways to control lawn weeds without the use of chemicals, and they work to varying degrees.
First: if a person wants to control the weeds in their lawn it makes the most sense to insure that the plant you want to grow there, namely grass, is thick and healthy. The better established the lawn grass is the less space, water, and nutrients are available to weeds. This can be done by improving the soil though the introduction of organic material (aka fertilizer,) aerating the soil, and keeping the thatch to a minimal level. The use of organics is good, especially o that last one, because the worms and such don't get killed off. You need them to help the soil break down and the dead grass and such to compost.
It is also a good idea to keep the grass a little longer to improve it's ability to survive the really hot weather of summer.
Second: Adjust the PH of the soil. Annoying weeds, such as dandelions, thrive at certain PH balances. Lower or raise, depending on the problem.
Third: Corn gluten. Corn gluten, a byproduct of corn production, has a great ability to keep weed seeds from germinating. According to studies, after several years, corn gluten can reduce weeds by about 90% and it's also good for the lawn.
Fourth: Try vinegar. If there are a few broad-leaf weeds, a solution of vinegar, water, and dish soap makes a great spray to eliminate the sporadic weed.
Fifth: Good old fashioned gloves and elbow grease. Pull out the weeds by hand.
As you can see, though poisons are perhaps faster at getting rid of weeds, keeping the grass healthy in the first place is the best natural remedy.