Preheat oven to 425°F. Slice a 1/4-inch strip from base and stem of squash, so it will sit flat. Peel squash, cut in half lengthwise and scoop out seeds. Cut flesh into 1/2-inch cubes. Place squash on a large, rimmed baking sheet, toss with 1 Tbsp. olive oil and sprinkle with salt and pepper. Roast, stirring once, until squash is tender and browned, about 20 minutes.
Warm a large skillet over medium heat. Cook bacon, stirring, until crisp, about 5 minutes. Using a slotted spoon, transfer bacon to a paper towel-lined plate. Pour bacon fat from pan; discard drippings.
Add remaining oil to skillet; return to medium heat. Add pepper flakes; stir for 15 seconds. Add sage and squash and sauté until heated through and sage is crisp, about 1 minute. Remove pan from heat.
Bring a pot of salted water to a boil. Drop pasta into boiling water and cook until al dente, 7 minutes or as package label directs. Drain pasta, reserving 1/2 cup cooking water.
Add pasta to skillet with 1/4 cup pasta water and lemon juice. Toss over medium heat until well coated, adding more water if needed. Season pasta with 1/4 tsp. salt. Divide pasta among 6 bowls and sprinkle with reserved bacon.