Heat oven to 200C/180C fan/gas 6. Push lemon halves inside the chicken’s cavity - they should all fit if you fiddle them around. Sit chicken in a smallish roasting tin, smear butter over the breasts and season well. Roast, breast-side up, for 30 mins, then flip over and roast, breast-side down, for a further 1 hr 30 mins-1 hr 40 mins until the chicken is cooked through and juices run clear when you pierce the thigh with a knife.
With 30 mins to go, pour all juices from the tin into a jug. After juices and fat separate, spoon 50ml fat from the top into a big, wide pan. Add the celery, onion and fennel, and soften gently for 20 mins.
When the chicken is done, pour any more juices into the jug. Reserve an extra 2 tbsp fat (see Nearly spring greens, related recipes) and discard remaining fat. On the heat, stir the flour into the veg until absorbed, then gradually stir in the stock and chicken roasting juices, simmering to a sauce. Stir in cream and parsley, remove from the heat and season.
Shred chicken from the carcass in large-ish chunks, discarding skin - if the bird is still hot, use clean rubber gloves or 2 forks. Juice the roasted lemons, pick out the seeds and stir all the juices and roasted pulp into the sauce with the chicken. Taste and season with a squeeze more juice from the final lemon if it needs it. Tip into a large pie dish.
Roll out the pastry on a flour-dusted surface until big enough to cover the pie. Brush the rim of the dish with beaten egg and lift on the pastry. Trim edges, then press and crimp to seal. Brush all over with more egg and bake for 30-40 mins until golden and crisp.