Preheat the oven to 400˚F. Butter an 8-inch springform pan and set aside.
In a medium stockpot, add the lemon juice, sugar, and 2 quarts of water. Bring to a boil over high heat. Prepare a large bowl of ice water and set aside.
Meanwhile, prepare your apples: Cut each apple into quarters and remove the cores from each piece. Slice each quarter as thinly as possible into (about 1/8 – 1/16-inch) half moons. Add the apple slices to the boiling water, reduce to a gentle simmer, and cook until just softened, but not falling apart, about 3 – 4 minutes. To test if the apples are done, remove a slice and bend it with your fingers. If it bends without breaking, it is done. Remove the apple slices and plunge them into the ice water bath to stop the cooking. Immediately remove them from the ice water and spread on a paper towel-lined baking sheet. Lightly dab the top of the apples with more paper towels to absorb excess moisture.
On a lightly floured work surface, roll the first sheet of puff pastry into an approximate 10 x 12-inch rectangle. With the longest side of the rectangle closest to you, cut the pastry vertically into about 8 (1 ½ x 10-inch) strips. Lay the strips on a parchment-lined baking sheet, cover with plastic, and transfer to the refrigerator to cool. Repeat with the remaining sheet of puff pastry.
To assemble the tart: Remove 1 strip of pastry from the refrigerator. With the strip placed in front of you horizontally, spread about 1 ½ – 2 teaspoons of caramel evenly over its surface. Working from left to right, arrange 5 apple slices in a row, overlapping each just slightly, and making sure the curved edges of the slices are slightly higher than the top edge of the pastry strip. Fold the bottom half of the pastry up over the bottoms of the apple slices, so that the pastry strip is folded in half lengthwise, and the apple slices are secured in place. Working carefully so the apples stay in place, roll the strip from left to right to form a flower. Place the flower, apple side up, into the buttered springform pan against the side to keep it from unraveling.
Repeat this step, snugly fitting each flower into the pan until you cannot fit anymore. (You should be able to fit approximately 12 – 14 flowers in an 8-inch pan). Cover with plastic wrap and place in the refrigerator to chill for 15 – 30 minutes.
Once chilled, remove the tart from the refrigerator and uncover. In a small bowl, combine the sugar and cinnamon. Scatter the cubes of butter over the tart and then sprinkle the cinnamon-sugar mixture evenly over the top. Place the tart pan on a rimmed baking sheet (to catch any potential leakage) and bake in the preheated oven for about 1 hour – 1 hour, 15 minutes, or until the pastry in between the flowers is completely cooked through. Remove from the oven and place on a wire rack to cool for 5 minutes.
After 5 minutes, carefully run a kitchen knife between the tart and the edge of the pan. Unlock the springform pan and transfer the tart to a serving dish. Drizzle with some more caramel to garnish and enjoy while warm.