Trim the leeks, discarding the roots and the tough tips of the leaves. Slice the leeks into rings about as thick as a pencil, then pile into a colander and wash very thoroughly in cold water.
In a large saucepan, melt the butter, stir in the leeks and cover the surface with a piece of greaseproof paper or baking parchment. This will help the leeks to cook in their own steam without browning. Cover with a lid and leave to simmer gently.
Peel and finely dice the carrots and add to the leeks, then finely dice and stir in the celery. Continue cooking for about 10 minutes, until the vegetables are tender.
Cook the lentils in boiling, lightly salted water for about 15 minutes, until tender but not soft. Drain and set aside.
Stir in the vegetable stock and the miso paste and continue cooking for about 10 minutes.
Wash the greens, roll them up and shred into ribbons. I like to keep them quite wide, like pappardelle. Stir them into the soup and continue cooking for 3 or 4 minutes until the greens have relaxed. Finely grate the lemon and stir into the leek soup and check the seasoning, adding salt and black pepper.
Ladle the soup into deep bowls, the lentils scattered over the surface.