Place oil in a large saucepan and heat over medium heat. When hot, sauté green onions and garlic. Add thyme, lemon juice, vinegar and pepper and cook a few more minutes. Add mushrooms and continue to cook until all liquid has evaporated. Allow to cool slightly and transfer to a food processor. Use the pulse button and process until coarsely chopped. Do not over-process. Serve at room temperature with low-sodium crackers.