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HEAT OVEN TO 350°.
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Combine butter, sugar, lemon juice and lemon peel in large mixer bowl.
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Beat at medium speed until creamy, about 1 to 2 minutes.
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Reduce speed to low.
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Add flour; beat until crumbly, about 1 to 2 minutes.
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Press dough evenly into lightly greased 8-inch square baking pan.
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Bake for 35 to 40 minutes or until lightly brown.
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Cool completely.
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Combine powdered sugar, 1 tablespoon butter and lemon juice in small bowl. Using wire whisk, mix until smooth.
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Spread thin layer of glaze over cooled shortbread; sprinkle with lemon peel.
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Let stand for 30 minutes to set.
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Cut into strips.