Flatten the dough into a disk, wrap well in plastic wrap and let it rest for at least 2 hours at room temperature or refrigerate for a day. (Let chilled dough sit at room temperature briefly before rolling.)
Plump the raisins with the rum in a small bowl, until all the liquor is absorbed.
Spread the breadcrumbs in a large heavy skillet and set it over medium heat. Stir and toss the crumbs until they begin to color. Lower the heat a bit and keep stirring until they're deep golden brown, then quickly spill the crumbs into a bowl, before they burn. Sprinkle ½ teaspoon cinnamon over the hot crumbs and toss in. When the crumbs cool completely stir in 10 tablespoons sugar.
In the same skillet, again over medium heat, stir together the chopped walnuts and 2 tablespoons sugar, until the sugar caramelizes and coats the nuts. Immediately spill into a bowl to cool.
Rinse and dry the lemons, remove their zest with a fine grater and squeeze out and strain their juice. Peel, core and cut the apples in thin slices and toss in a large bowl with the lemon zest and juice, the remaining ¾ cup sugar and ½ teaspoon cinnamon. Toss in the plumped raisins, mix well and let the apples steep in the sweetened fruit juices.
Arrange a rack in the center of the oven and heat it to 425 degrees F. With a pastry brush, lightly coat the parchment in the sheet pan with a tablespoon or 2 of soft butter.
On a large, lightly floured work surface, start rolling the strudel dough into a rectangular shape, turning it over frequently and dusting the surface with flour as needed. When it becomes a thin sheet, stretch it with your hands, both on the table and as you lift and turn it over. Gradually roll and stretch the rectangle until it's about 30-inches on the long sides and 20- inches on the shorter sides. Trim thick edges with a knife or pizza cutter.
Now arrange the linen cloth on the table -- under the dough sheet -- to roll up the strudel. If someone can assist you, hold the dough sheet in the air while the cloth is placed flat and smooth on the work surface. Line up a long edge of cloth with the edge of your counter. Lay the dough flat on top of the cloth, with its long side left to right in front of you, set in a few inches from the edge of the cloth and. (If you DON'T have a helper, lay out the cloth on another surface and move the dough rectangle over to it.)
When the cloth and the dough are in place, brush the entire surface of the dough with 4 tablespoons or so of soft butter. Sprinkle the bread crumb mixture evenly all over the dough then scatter the caramelized walnut pieces on top.
Next, lift the apple slices from the bowl, letting excess juices drain off, and heap them in a narrow row, running left to right, set in about 3 inches from the long edge of dough near you. Make the row straight and compact and slightly shorter than the dough, sheet, so there are several inches of bare dough on the left and right sides of the apple row.
To roll the strudel, grasp the edge of the cloth and lift it, bringing the uncovered margin of dough against the apples. Hold the cloth close to the filling, so you have good control, then lift and push it forward, rolling the entire row of apples over and wrapping it snugly in dough. Keep rolling to wrap all the dough around the strudel, forming a long neat log. Twist the unfilled flaps of dough on the ends of the log, so they're snug against the filling, then trim and tuck them under the strudel.