You can use Vegan Mayo, or unsweetened Vegan Yogurt. I like to do half and half. The Trader Joe's Cashew Yogurt is my favorite right now.
Then, simply whisk all the ingredients together, taste and adjust for seasoning. I like my sauces TANGY, so start with the smaller amounts of things like Lime Juice and add more as you like.
You can also blend this up in a food processor or an immersion blender for a smoother consistency.If the sauce is thin, you can blend in 1/8 tsp of Xanthan Gum to thicken. Just add it as the food processor / blender is running.