Preheat oven to 150C. Halve leeks lengthways, then crossways and place in a single layer in a deep baking dish, cover with water then season to taste with sea salt and lemon juice. Cover with foil and bake until leeks are tender (35-40 minutes).
For vinaigrette, combine all ingredients in a jar, seal and shake vigorously until emulsified, and season to taste.
Drain leeks from poaching liquid, arrange on serving plates with radish and celery leaves, drizzle with vinaigrette, scatter with cheese and walnuts and serve.