Remove the pits from the kalamata olives and discard. Transfer the kalamatas and regular olives to the work bowl of the food processor.
Zest the lemon and squeeze out 1 tablespoon of the lemon juice.
Add the capers, garlic, anchovies, lemon zest, 1 tablespoon of lemon juice, crushed red pepper flakes, thyme and olive oil.
Secure the lid and pulse to process the the tapenade until relatively smooth and well blended. Taste for seasoning... If you want more heat, add more red pepper flakes, for more acid, add lemon juice or for more briny flavor add a few additional kalamata olives.
Transfer to a small bowl and serve with crackers, crudite or on a meze platter.