Preheat oven to 325°F (163°C). Grease a bundt pan thoroughly with shortening and dust with flour, tapping out excess.
Cream together the softened butter and granulated sugar until light and fluffy — about 3–5 minutes with an electric mixer on medium speed. Scrape the bowl as needed. Add the eggs one at a time, beating well after each addition.
Add the flour gradually, mixing on low until just combined. Stir in the lemon extract. Pour in the 7UP and fold gently until the batter is smooth.
Fold in the chopped maraschino cherries gently with a spatula.
Pour batter into the prepared bundt pan and bake for about 1½ hours, or until a toothpick comes out clean.
Cool the cake in the pan for 10–15 minutes. Invert onto a plate and poke holes in the top. Pour reserved cherry juice over the cake.
Let the cake cool completely. To make the glaze, whisk together powdered sugar, lemon extract, and milk until smooth. Drizzle over the cooled cake.
Notes
For a deeper cherry flavor, warm the reserved cherry juice before pouring it over the cake.