Put a large pan onto a medium heat and add some olive oil, break the lobster shell into the pan. Then add a bay leaf, the celery, whole peppercorns, sprigs of thyme, shallot, some more olive oil, the water and the white wine.
Cover the pan and allow it to simmer for 30 minutes. Line a colander with some muslin and place it into a bowl. Strain the stock through the muslin into the bowl, the stock will keep for up to 2 days in the fridge or you can freeze it, for up to 8 weeks.