Cook the tagliatelle in a large saucepan of lightly salted boiling water for 8 minutes, or according to packet instructions, until al dente.
Meanwhile, heat the oil in a deep-sided frying pan and fry the pork strips for 6–7 minutes, until golden. Remove with a slotted spoon and set aside in a bowl.
Add the mushrooms to the pan and cook for 3–4 minutes, until soft and golden. Remove and add to the pork.
If using the lemon, arrange the slices in a single layer in the pan and cook for 2–3 minutes, turning once, until golden. Remove and set aside.
Pour the wine and tarragon into the pan, and bubble to reduce by half. Return the mushroom and pork to the pan and pour in the cream. Season well. Simmer gently for 2–3 minutes, until thickened slightly, then serve immediately alongside the tagliatelle, garnished with the lemon slices.