In a mixing bowl, combine the tahini, water, 3 tablespoons of lemon juice, garlic, vinegar, and salt. Use a small whisk to stir it all together until it is creamy. Taste and add another tablespoon of lemon juice if a more tart flavor is desired. (You can also add up to another 1/4 teaspoon of salt, to help make the flavor pop.)
Stir in the fresh dill, and let the dressing rest for at least 15 minutes to let the flavors meld. Serve immediately, or store it in an airtight container in the fridge for up a week.
The dressing will thicken quite a bit once it has been in the fridge, so you may want to thin it out with 1-2 tablespoons of water the next time you serve it.
Look for raw tahini that has no added oil for the best flavor and results. The only ingredient on the label should be sesame seeds (or hulled sesame seeds). There's a tahini recipe here on my website if you would rather make your own!