Line a greased 15x10x1-in. baking pan with waxed paper and grease the paper; set aside. In a large bowl, beat egg yolks until lemon-colored. Gradually beat in 1/4 cup sugar. Stir in oil and lemon extract; set aside.
In another large bowl, beat egg whites on medium speed until soft peaks form. Gradually add the remaining sugar, 2 tablespoons at a time, beating until stiff glossy peaks form and sugar is dissolved. Fold into egg yolk mixture. Combine the flour, baking powder and salt; fold into egg mixture.
Transfer to prepared pan. Bake at 375° for 10-12 minutes or until cake springs back when lightly touched. Cool for 5 minutes. Turn cake onto a kitchen towel dusted with confectioners' sugar. Gently peel off waxed paper. Roll up cake in towel, starting with a short side. Cool completely on a wire rack.
For filling, in a small bowl, combine the milk, lemon juice, lemon zest and 5 drops of food coloring. Fold in whipped topping. Unroll cake; spread half the filling over cake to within 1 in. of edges. Roll up again. Place seam side down on a platter. Spread remaining filling over cake.
In a small bowl, combine water and remaining food coloring; add coconut. Stir until coconut is evenly tinted. Sprinkle the coconut over cake. Refrigerate for at least 2 hours before serving. Refrigerate leftovers.