Experts and BHG readers answer.
No. There is no organic equivalent to the synthetic "weed B gone" types of chemicals that kill broadleaf weeds but leave grass unharmed.
For an organic approach, try this: apply a corn gluten product this spring to prevent annual weeds like crabgrass and foxtail. In NC, now's the time, or it might even be a little late, so you'll need get going. Garden centers usually carry corn gluten.
Then, for existing perennial weeds like dandelion, a weed tool is pretty much your best option. It seems intimidating at first if you have a lot of weeds, but think of it as a long term project and keep at it. You will eventually make progress.
Some weeds, clover in particular, are next to impossible to control by hand. All I can suggest is living with it. Frankly, there's nothing inherently wrong with having clover in your yard (it doesn't look bad, and it even adds nitrogen to your soil!). With an organic approach, my opinion is that this is an instance where it's better to just let it go and live with it.
Some people advocate using nonselective approaches (boiling water or torches, for example), but i think this is wholly unacceptable for lawns. Great for other areas, but in lawns, leaving dead spots all over the place just to remove some dandelions is like cutting off your nose to spite your face.
Meanwhile, mow your lawn at 2-3 inches, don't neglect fertility, and a good thick healthy lawn should keep weeds down (not gone, but much less).