Place an oven rack in the center of the oven. Preheat the oven to 200 degrees F.
For the vegetables: Place a grill pan over medium-high heat, or preheat a gas or charcoal grill. Drizzle the vegetables with olive oil and season with salt and pepper. Grill the eggplant until tender, about 4 minutes each side. Grill the asparagus for 3 to 4 minutes, turning occasionally until crisp-tender. When cool enough to handle, cut the asparagus in half crosswise.
For the filling: In a small bowl, mix together the ricotta cheese, basil, Pecorino Romano, lemon zest, and lemon juice until smooth. Season with salt and pepper, to taste.
To assemble: Place 4 slices eggplant on a work surface. Spread each with 2 to 3 tablespoons of the ricotta mixture. Line 4 pieces of asparagus, side-by-side, on top. Place another slice of eggplant on top and repeat the layers. Top each napoleon with a slice of eggplant and place on a small baking sheet. Bake until warmed through, about 10 minutes, and serve.
If the eggplant slices dry out in the oven, drizzle with olive oil before serving.