Preheat oven to 400 degrees. On a rimmed baking sheet, place squash cut side down; cover sheet tightly with aluminum foil. Bake until squash is easily pierced with the tip of a paring knife, 45 to 55 minutes.
Meanwhile, in a medium bowl, combine onion, 1 tablespoon oil, lime zest and juice, 1/2 teaspoon coarse salt, and 1/8 teaspoon ground pepper. Let stand until onion is softened,
at least 15 minutes.
When squash is about 10 minutes from being done, heat a large skillet over medium-high. Season steaks with salt and pepper. Place 2 steaks in skillet, and cook until medium-rare, 2 to 3 minutes per side. Transfer to a plate, and cover loosely with foil; repeat with remaining steaks. Let rest at least 5 minutes.
Meanwhile, holding squash over a medium bowl, use a fork to scrape flesh into strands. Drizzle with remaining 2 tablespoons oil; season with salt and pepper, and stir to combine. Top steaks with pickled onion, and serve with squash.