Carve a line or a cross into the top of each chestnut, and cook in a dry, hot pan tossing, for 10-15 minutes until the flesh is tender. Peel and discard the skins.
In the meantime, heat 1 tablespoon of the olive oil and sauté the pancetta slices for 1 minute on each side. Toss in the walnuts to slightly toast in the olive oil-pancetta fat.
Place the mixed greens in a salad bowl, add the walnuts, chestnuts, and pancetta. Season with salt and pepper.
Drizzle with the remaining olive oil and lemon juice, and serve.