So I think you are going to have to make the decision that the lazy way doesn't really work so well first.
the best and most organic method to rid a lawn of weeds (any weeds, we in
permaculture actually don't think there are any "weeds") will be to build a healthy lawn of grass plants.
To build really good grass plants you would first loosen the soil (broad fork or other method to open the soil and let air down in).
second you would cut the grass plants at 3"-3.5" so they provide shade to the soil they grow in.
third you would nourish the soil so the grass plants have proper nutrition.
Now you have the start of a healthy, mostly weed free lawn. The next step could be using a spot sprayer filled with vinegar and a tablespoon of oil and spray each "weed" individually, being careful to not get this mix on your grass plants. (vinegar is a non-discriminate killer of plants)
for more ideas on weed killers that are natural and organic in nature try this site
organic weed control