If the lamb mince is relatively lean, heat the olive oil in a large frying pan, skillet or casserole over a medium-high heat. Add the mince and cook until well browned, breaking it up with a wooden spoon. Drain off any excess fat, reserving a little for cooking the vegetables, then transfer the lamb to a plate or bowl.
Add a little of the reserved lamb fat to the same pan, followed by the onion, carrot and celery. Cook over a medium heat for 6-8 minutes, stirring occasionally, until softened. Add the garlic and cook for a further minute.
Return the browned lamb to the pan. Stir in the tomato purée and cook for 1-2 minutes before pouring in the red wine, scraping up any caramelised bits from the bottom of the pan. Allow to bubble for a few minutes, until noticeably reduced.
Add the chopped tomatoes, stock, Worcestershire sauce, oregano, and rosemary. Season with salt and freshly ground black pepper.
Bring to a gentle simmer and cook uncovered for 25-30 minutes, stirring occasionally, until the ragù is rich and thick. Remove and discard the bay leaf.
Meanwhile, make the Caerphilly béchamel. Melt the butter in a saucepan over a medium-low heat. Add the flour and stir continuously for 1-2 minutes, then gradually whisk in the milk, adding a little at first and whisking until smooth before adding more.
Once all the milk has been incorporated, cook gently, whisking regularly, until the sauce has thickened. Remove from the heat and stir in 150g Caerphilly until melted. Add the nutmeg and season with salt and freshly ground black pepper to taste.
Preheat the oven to 180°C fan / 200°C conventional. Spread a thin layer of lamb ragù over the base of the baking dish and top with a layer of fresh lasagne sheets. Add another layer of ragù followed by Caerphilly béchamel. Repeat with another layer of pasta, ragù and béchamel.
Finish with a final layer of fresh lasagne sheets and the remaining béchamel, making sure the pasta is completely covered.
Scatter over the remaining 50g Caerphilly.
Bake uncovered for 30-35 minutes, until bubbling, golden brown and the pasta is tender. Remove from the oven and leave to rest for 10-15 minutes.
Garnish with the fresh thyme leaves, then slice and serve.