Cut ½ inch from both ends of the squash and cut in half lengthwise.
Microwave the squash on a plate, cut-side down, on high until tender, 10 to 12 minutes. Let cool for 5 minutes.
Meanwhile, heat 1 tablespoon of the oil in a large skillet over medium-high heat. Season the lamb with the cumin, ½ teaspoon salt, and ¼ teaspoon pepper.
Cook the lamb to desired doneness, 4 to 5 minutes per side for medium-rare.
Scoop out and discard the squash seeds. With a fork, gently scrape the strands of the flesh into a bowl.
Toss the squash with the scallions, mint, remaining 2 tablespoons of oil, ½ teaspoon salt, and ¼ teaspoon pepper. Serve with the lamb.