Preheat a grill or grill pan to medium-high heat. Grill the sausages, covered with a medium heatproof bowl, until nice and charred and no longer pink on the inside, flipping once, 6 to 8 minutes per side. Transfer to a cutting board, let cool slightly, then slice on the bias. Set aside.
Meanwhile, bring a large pot of water to a boil. Poach the garlic cloves in the boiling water for 5 minutes, then transfer them with a slotted spoon to a food processor. Add the pasta to the boiling water and cook to al dente according to the package directions.
Meanwhile, add the walnuts to the food processor with the garlic and pulse until chopped, about 8 times. Add the spinach, basil, cheese, olive oil, raisins, salt, pepper and lemon zest and juice. Pulse about 10 times, until combined but still rustically chopped. Season with additional salt and pepper if needed.
Heat a large skillet over medium heat. Using a spider, add the pasta to the skillet. Add the spinach pesto and toss to combine. Heat until warmed through. Season to taste if necessary and serve immediately topped with grilled sausage slices.