Cook the Puy lentils in boiling water for 20-30 minutes or until tender. Drain them in a colander and spread on a tray to dry.
Warm the olive oil in a saucepan and sweat the carrot, celery, leek, garlic and ginger until soft. Add the seasoning and cook for 2-3 minutes. Stir in the lentils, then add the stock and bring to the boil.
Add the tomatoes and two tablespoons of the chopped coriander or chervil. Check the seasoning. Simmer for 30 seconds, or until you have a loose sauce (not too wet, not too dry), then remove from the heat.
Heat the sunflower oil in a frying pan or ribbed cast iron pan until very hot, then add the monkfish fillets. Fry them until well browned on both sides. If you leave them for 2-3 minutes before turning to cook the other side, this should prevent sticking.
Remove the monkfish from the pan. It should be brown on the outside but still soft in the centre. Leave it to rest on a baking tray and season with salt, pepper and lemon juice.
Stir the crème fraîche into the lentils, which should be looking nice and rich by now.
Divide the lentils between four warmed serving bowls, making sure the sauce is evenly distributed. Cut each piece of fish into 6-8 slices and place on top of the lentils.
Garnish with the rest of the chopped coriander and the other chopped herbs and serve at once.