Mix together brown sugar, oil, eggs, lemon peel and 2 tablespoons of lemon juice until well combined. Add flour, baking soda, salt, zucchini and walnuts; stir just until combined.
Spread evenly in ungreased 10 x 6 micro-safe baking dish. Microwave on medium-high 70%, uncovered for 7 minutes, rotating the dish once.
Then microwave on high 2 1/2 to 3 minutes or until no longer doughy, rotating the dish once. Cool completely.
Combine powdered sugar and butter in micro-safe bowl. Microwave on high, uncovered for 15-20 seconds or until butter is softened. Blend in the remaining lemon juice and enough water until it's a spreading consistency. Spread over bars and cut into squares.