Beat oil, butter, sugars, lemon juice, vanilla and almond extract in large bowl with electric mixer at medium speed until creamy.
Combine flour, cream of tartar and baking soda in separate bowl. Gradually beat into butter mixture until stiff dough forms.
Drop dough by rounded tablespoonfuls 2 inches apart onto prepared cookie sheets; flatten gently with fork. Bake 20 minutes or until cookies brown around edges only. Cool cookies on cookie sheets 1 minute. Remove to wire racks; cool completely.