Preheat oven to 450°F (230°F).
In a large mixing bowl, combine squash, Brussels sprouts, oil, salt and pepper. Mix thoroughly and transfer to a heavy-duty baking sheet lined with parchment paper. Bake on lower rack, stirring twice, until browned and soft, about 25 minutes. Remove from oven.
Lower temperature to 350°F (180°F).
While the vegetables are roasting, whisk vinegar, water, sugar and a pinch of salt in small bowl until sugar is dissolved. Stir in shallot. Set aside, stirring occasionally.
Line a heavy-duty rimmed baking sheet with foil. Spread out half the chips and sprinkle with half the cheese, half of the roasted vegetables, cranberries and thyme. Repeat with a second layer using up remaining half of chips, cheese and toppings. Bake until cheeses are melted and nachos are hot, 15 to 20 minutes.
Remove from oven. Drain shallots and sprinkle over nachos. Serve immediately with lemon wedges.