Peel the cucumber and scoop out the seeds. Grate the cucumber on the large holes of a box grater or finely dice it. Place the grated cucumber in a clean dish towel and squeeze out the excess liquid.
In a medium bowl, mix together the coconut yogurt, mint (or dill), garlic, 2 tablespoons of extra virgin olive oil, and lemon juice.
Add the diced cucumbers and stir well. Season to taste with salt and pepper.
Drizzle the remaining tablespoon of extra virgin olive oil on top of the dairy-free Tzatziki sauce.
Notes
The sauce can be kept in the fridge for up to 2 days.