Sift flour, 2 1/3 cup white sugar, baking powder, and salt together in large bowl. Whisk 1 1/2 cups milk and eggs together in another bowl; add vegetable oil, 1/2 cup lemon juice, 1 tablespoon lemon extract, and 2 teaspoons vanilla extract to milk mixture. Continue to whisk until smooth and syrup-like. Stir flour mixture into milk mixture and pour into a fluted tube pan (such as a Bundt®).
Bake in preheated oven until a toothpick inserted into the center comes out clean, about 1 hour 20 minutes. Allow cake to cool for 10 minutes. Run a paring knife between the cake and the edge of the pan. Hold the cake pan on its side and gently tap the sides of the pan against the counter to loosen it. Cover cake pan with a plate and invert it to tip the cake out of the pan and onto plate.
Heat confectioners’ sugar and 1/4 cup white sugar, orange juice, 2 tablespoons milk, 1 tablespoon lemon extract, 1 tablespoon lemon juice, and 1/4 teaspoon vanilla extract in a small saucepan over medium heat until mixture comes to a foamy boil. Remove from heat immediately and stir until foam disperses, about 1 minute. Drizzle mixture over hot cake and allow glaze to harden, 10 to 20 minutes.