Heat oven to 200C/180C fan/gas 6. Slice the peeled potatoes as finely as possible on a mandolin, with the fine slicing blade of a food processor, or with a very sharp knife. (The more finely you slice them, the quicker and more evenly they will cook.)
Pat the potatoes dry with a clean tea towel and tip into a large bowl. Pour over the melted lactose free butter, sprinkle over the thyme and some salt (preferably sea salt or rock salt), and toss until each slice is coated in butter.
In a roasting tin, measuring about 20 x 20cm, assemble the potato slices vertically, tightly packed together like a deck of cards, until the dish is full and you’ve used all the potatoes.
Sprinkle with a little more salt and place in the oven for 45-50 mins until crisp and cooked. Use a skewer or small sharp knife to check that the potatoes are completely soft and cooked in the centre. Serve from the tin alongside the lamb.