Rinse the salmon and pat it dry. Trim the thin ends and sides to create a neat rectangular shape, reserving the scraps to cook for something else, such as pasta or salad. Rub the salmon, both the skin and the fish, with the oil, salt, and pepper. Cut the rectangle in half to create 2 squarish pieces.
Place 4 lengths of kitchen string (each about 18 inches) on a work surface perpendicular to you and parallel to one another, spacing them about 2 inches apart.
Place half the dill sprigs on the strings, placing the dill perpendicular to the strings. Place a square of salmon on the dill, skin-side down. Place a quarter of the lemon slices along the center of the salmon and then press the bread crumb mixture onto the lemon and salmon. Make another row with 1/3 of the remaining lemon slices along the top of the bread crumb mixture. Place the other square of salmon on top, skin-side up, placing the thick end of the top piece over the thin end of the bottom piece so you get a roughly even thickness all over.
Cover the salmon with the remaining dill sprigs and tie the strings, securing the salmon squares together. Don't tie the salmon too tightly. You want it just secure enough to hold everything in place.
Generously oil a roasting pan just large enough to hold the salmon. Arrange the remaining lemon slices in the pan and place the stuffed salmon on top of them. Bake for 30 to 35 minutes if you like the salmon to be a little rare in the middle. If you don't care for salmon this rare, roast it a little longer.
Let the salmon rest for 5 minutes. Transfer it to a platter and cut the strings. Slice the salmon with a sharp knife into fillets—it will fall apart as you do so—and make sure you scoop up ample stuffing and lemon with each fillet.