Preheat the oven to 350°F (175°C). Grease a 10 x 3 ½ inch (25 x 9 cm) bundt pan. Bring 1 ½ cups (350 ml) of water to a boil, remove from the heat, add the tea, and steep for 5 minutes; strain, pressing to extract as much liquid as possible. Melt the butter; stir it together with the brown sugar, molasses, and corn syrup until blended. Set aside to cool. Combine the flour, ginger, cinnamon, cloves, nutmeg, and salt in the bowl in a food processor and pulse to blend. Scrape in the butter-sugar mixture and blend. Add the eggs and lemon zest and process until smooth.
Stir the baking soda into cup (240 ml) of the tea. It will bubble up. Stir the mixture into the batter, mixing well; then scrape it into the prepared pan. Bake for 40 to 45 minutes until the top is springy and a knife inserted near the center comes out clean. Remove the pan and cool on a cake rack. Combine the remaining tea with the lemon juice. Sift in the confectioners’ sugar, whisking until you have a thick but spreadable icing. Pour over the cooled cake and let it set.