Melt the butter in a frying pan set to medium heat. Add the onions and celery and cook for 2 minutes. Add the salt, pepper and flour and cook for 3-4 minutes.
Pour in the chicken stock and bring it to a boil. Reduce to low heat and simmer until the stew thickens, 8-10 minutes. Add the milk and cook for an additional 4 minutes.
Remove the pan from the heat and add the potatoes, carrot, peas, corn, lobster and tarragon. Season with more salt and pepper, if desired. Pour the stew into 6 ramekins.
Cut the pie crust into 6 circles that are slightly bigger than the rim of the ramekins. With the remaining pie crust, cut out 6 hearts and gently press one heart onto the center of each circle of dough.
Place the crust on top of the ramekins and tuck the edges of the crust into the edges of the ramekins with a fork. Gently make two slits on either side of the hearts, then brush with the beaten egg. Place the ramekins on a baking sheet and bake at 400F for 35-40 minutes until the crust is brown and crispy.
Remove from the oven and let cool 5 minutes before serving.