Preheat oven to 200°. Line a large rimmed baking pan with parchment paper.
Arrange tortilla chips in a more-or-less single layer on pan. Sprinkle with 2 cups cheese and bake until melted, about 5 minutes.
Loosen chips from parchment and scoot onto a large heatproof platter. Spoon chili over chips, then sprinkle with remaining 1 cup cheese. Return to oven to melt cheese, about 3 minutes.
Meanwhile, in a small bowl, whisk sour cream with lime juice and a couple of pinches of salt (to taste). Spoon into a squirt bottle, or spoon into a small sealable plastic bag and snip off a bottom corner to make a tiny (1/4-in.-wide) hole. Drizzle sour cream over nachos, dust with smoked paprika, and top with green onions. Serve with hot sauce if you like.