Getting the PH down to 6.5 might help according to this site:
My approach is to keep the lawn healthy and apply fertilizer early (February in the Raliegh NC area) to give the grass a head start. I use 2,4D in weed and feed if I have a big investation. So, I don't have any real hands on experience with avoiding chemicals.
I applied a thin layer of a combination of mushroom compost, and aged steer manure to portions of my lawn a few months ago. The areas that received the compost/manure DO NOT grow dandelions now.
The downsides with this approach is it is labor intensive. The cost of organic material. And it will make your grass grow really fast.
The upsides are its labor intensive and good exercise. The grass grows really fast, healthy and green. And you're not spreading poison. Plus, its building the soil up so the grass will be healthier and in time theoretically will be able to resist weeds on its own.
Think of it as investing in your lawn.