For the cake: Position a rack in the lower third of the oven and preheat to 350 degrees F. Butter and line the bottom of 9- by 13-inch cake pan with parchment paper, overlapping on two sides to create flaps.
Put the chopped chocolate in a bowl. Heat the cola just to a simmer over low heat and pour over the chocolate. Let stand for 5 minutes; stir until smooth.
Whisk together the flour, cocoa powder, baking soda and salt in a medium bowl. Beat the sugar and eggs in a separate bowl with an electric mixer on medium speed until slightly thickened and pale, about 3 minutes. Gradually add the buttermilk, oil, vanilla and melted chocolate to the eggs. Beat on low until combined, but not aerated. Add the flour mixture and continue to beat until just combined. Stir lightly with a rubber spatula to remove any pockets of flour. Pour the batter into the prepared pan and bake until the cake springs back lightly when touched and a tester inserted in the center comes out clean, about 40 minutes.
Cool the cake completely in the pan on a rack. Run a knife around edge of the pan and invert the cake onto the rack. Carefully remove the parchment paper and cool completely. (The cake may be made in advance, tightly wrapped and kept at room temperature for up to 2 days.)
For the icing: Bring a few inches of water to a boil in a saucepan that can hold a standing mixer's bowl above the water. Whisk together the sugar, lemon juice, salt and egg whites in the bowl by hand. Set the bowl above the boiling water and continue whisking until the mixture is hot to the touch and the sugar dissolves, 1 to 2 minutes. Transfer the bowl to a standing mixer fitted with the whisk attachment and beat the whites at medium-high speed until they almost hold a stiff peak and are fully cooled, about 10 minutes. Beat in the butter, a little at a time, until the icing is smooth and spreadable. (If the icing separates, just keep beating and it will come back together.)
Frost the cake. Serve or set aside at room temperature for up to 2 hours before serving, refrigerating if needed. (If cake is refrigerated, bring to room temperature 1 hour before serving.)