Step 1Clean mushrooms with damp paper towel. Cut off stems and discard; set caps aside.
Step 2Combine oil, 2 tablespoons lemon juice, 1/2 teaspoon salt and pepper to taste. Brush mushroom caps with marinade and let stand 15 minutes.
Step 3Grill mushrooms gill side up over medium heat on covered grill until tender, 5 to 6 minutes. Pat excess moisture from center of mushrooms with paper towel and place gill side up on serving platter.
Step 4Cut each avocado in half and remove pit. Peel and mash with fork in bowl. Stir in chipotles, onion, 2 tablespoons lemon juice and 1 1/2 teaspoons salt.
Step 5Spoon avocado mixture onto mushrooms. Sprinkle each with queso fresco.