Preheat the oven to 425 degrees . Line a baking sheet with parchment paper. In a medium bowl, whisk together 1 1/3 cups milk and the lemon juice; let sit at room temperature for 10 minutes.
Meanwhile, in a large bowl, combine the flour, baking soda and salt. Rub in the butter until coarse crumbs form, about 3 minutes. Stir in the cranberries.
Beat the egg into the milk mixture; stir into the flour mixture until just combined. Transfer the dough to a lightly floured surface and knead until it just comes together; form into an 8-inch round and place on the prepared baking sheet. Using a knife, score a 1/2-inch-deep "X" in the round. Bake until dark golden and crusty, 25 to 30 minutes. Transfer to a rack to cool completely.
Meanwhile, in a medium bowl, combine the confectioners' sugar, lime peel, lime juice and the remaining 1 tablespoon milk. Drizzle the cooled soda bread with the lime glaze.