In a large bowl, cream butter and sugars until light and fluffy. Beat in the egg, cherry and lemon juices and vanilla. Combine dry ingredients; gradually add to creamed mixture and mix well. Stir in nuts and cherries.
Shape into four 12-in. rolls; wrap each in plastic wrap. Refrigerate for 4 hours or until firm.
Unwrap and cut into 1/4-in. slices. Place 2 in. apart on ungreased baking sheets. Bake at 375° for 8-10 minutes or until the edges begin to brown. Remove to wire racks to cool.
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