Preheat the grill. With a sharp knife, cut the lobster tails in half down the middle. Place on a baking tray under the grill, shell side down, and cook 15 minutes. Remove and let cool. Remove the tail meat and discard shells.
Heat a splash of olive oil in a large saucepan over low heat. Add the vegetables, and cook, stirring, 10 minutes. Push the vegetables to the edge of the saucepan and fry the tomato paste for 15 seconds then stir in. Add salt, pepper, sugar and bay leaf. Saute another 10 minutes.
In a separate saucepan, heat the stock then add to the vegetables with the milk. Bring to a boil, lower heat and simmer 25 minutes.
Remove the bay leaf and blend the soup. Reheat, add the lobster meat, parsley and more pepper if desired. Simmer 5 minutes and serve.