Preheat oven to 350 degrees F (175 degrees C). Grease and flour a 10-inch Bundt pan.

To make the cake: Combine cake mix, pudding mix, eggs, oil, water, lemon juice, 1/4 cup tequila and 2 tablespoons triple sec in a large bowl; beat with an electric mixer until smooth and creamy, about 2 minutes.

Pour batter into prepared pan. Bake in the preheated oven until a toothpick inserted into the center of the cake comes out clean, about 45 to 50 minutes. Cool in pan for 10 minutes, then transfer to a cooling rack while you make the glaze.

To make the glaze: Combine confectioners' sugar, 1 tablespoon tequila, 2 tablespoons triple sec, and 2 tablespoons lime juice in a small bowl; mix until smooth. Pour glaze over cake while still warm.