Heat oven to 350°F, with one rack positioned in the center and one directly below; toast walnuts and anise seeds just until golden, 4 to 5 minutes, cool and chop together on a cutting board.
In a large bowl, whisk together flour,baking powder and salt.
In a separate bowl whisk together remaining ingredients (eggs, sugar, butter, oil,lemon peel,lemon juice) until smooth.
Stir egg mixture into flour mixture, then stir in walnuts and anise seeds; (Dough will be soft, that's okay).
Divide dough in half, lightly grease a large cookie sheet; with floured hands, shape dough into two 14x2-1/2-inch logs,slightly rounded in center; Bake on center rack until firm to the touch,30 minutes;let cool 20 minutes, (Leave oven on).
Transfer logs to a cutting board; with serrated knife,gently cut logs on a angle into 1/2-inch-thick slices; lay slices on 2 ungreased cookie sheets, bake until biscotti are lightly browned around edges, 10 minutes.
Flip biscotti over on cookie sheet reversing positions when you put them back in the oven; bake 10 minutes more, transfer biscotti to wire racks to cool.