1. Heat oil in a large skillet.
2. Sauté the onions for about 15 minutes or until edges are brown. Season to taste. Add mushrooms and thyme, if using, and cook until all the liquid has been released and evaporated and the mushrooms are very well browned, about 20 minutes. Season with salt and pepper to taste. Cool completely.
3. In the bowl of a food processor, pulse the olives and parsley until chopped. Add sautéed onions and mushrooms and pulse a few more times until all is well-chopped. Add in olive oil and lemon juice and pulse one to two more times until well-combined. Store in the fridge for up to one to two weeks.