In large bowl and using fingers, rub sugar with lemon rind until fragrant. Beat in butter until light. Beat in eggs, 1 at a time, beating well after each. Beat in lemon juice.
In separate bowl, whisk together flour, poppy seeds, baking powder, salt and baking soda; stir into butter mixture alternately with sour cream, making 3 additions of dry ingredients and 2 of sour cream. Scrape into 8 greased and floured 1-cup (250 mL) mini Bundt pans or 5- x 3-inch (625 mL) mini loaf pans, or one 9- x 5-inch (2 L) loaf pan.
Bake in 325°F (160°C) oven until cake tester inserted in centre comes out clean, about 30 minutes for Bundt pans, 1 hour for large loaf. Transfer pans to rack.
Icing: In small bowl, stir icing sugar with lemon juice until smooth. Divide in half.
Glaze: Stir lemon juice into one half of icing; brush over hot cakes. Remove from pans; let cool on rack. Drizzle with remaining icing, adding a little more lemon juice to loosen if necessary.