Bring a large pot of salted water to a boil; add 1 tablespoon oil. In a medium bowl, stir together ricotta, tarragon, and lemon zest; season with salt and pepper.
A few at a time, cook lasagna noodles until al dente. Using tongs, transfer to a baking sheet, laying each square flat. Cover with plastic wrap. Empty water and reserve pot.
In pasta pot, heat remaining oil over medium-high. Add garlic and cook until tender, 1 to 2 minutes. Add weeds; season with salt and pepper. Cook, tossing, until tender, 6 to 8 minutes. Stir in raisins and lemon juice; season with salt and pepper.
On each of four serving plates, top one lasagna noodle with about 1/4 cup weed mixture and 2 tablespoons ricotta mixture. Top with another noodle, 1/4 cup weeds, and 2 tablespoons ricotta. Drizzle with oil, if desired, and serve immediately.