Heat 2 tablespoons of the oil in the pan over a medium-high heat and fry the pork slices for 3–4 minutes, turning once so that they are browned on both sides. Remove with a slotted spoon.
Add the remaining oil to the pan, tip in the mushrooms and cook for 3–4 minutes, stirring occasionally, until softened and golden.
Cut half of the lemon into slices and add to the pan to brown a little on each side, then remove and set aside.
Return the pork to the pan, add the crème fraîche and tarragon and pour in the juice from the remaining lemon. Season well, bring to the boil, then reduce the heat and leave to bubble gently for 5 minutes. Add the prepared lemon slices at the last minute and gently stir through.
Serve the pork with white rice or crispy potato wedges.