Beat butter, sugar, lemon and vanilla together until creamy. Add flour and oats; mix well. Cover and chill in refrigerator about 30 minutes.

Heat oven to 350°F. Shape dough into 1" balls. Place 3" apart on ungreased baking sheets. Flatten with bottom of glass dipped in sugar.

Bake 12-15 minutes, or until edges are light golden brown. Remove from oven. Cool 1 minute on baking sheet; remove to wire rack. Cool completely and sprinkle with powdered sugar.