Zest and juice lemon into a small bowl. Add ¼ of minced garlic and a pinch of salt. Set aside. Roughly chop green olives. Pat shrimp dry and season with salt and pepper on all sides.
Bring a pot of salted water to a boil. Cook pasta until al dente. Drain and set aside, reserving ½ cup pasta water.
Meanwhile, heat olive oil in a skillet over medium heat. Stir in remaining garlic and then add shrimp and olives, cooking for one minute per side until the flesh is pink in color. Don’t worry if it’s not completely cooked through. Add vermouth to the pan and cook, stirring, scraping any bits off the bottom of the pan. Let it bubble a minute, then lower heat.
Stir in pasta, lemon mixture, and butter. Toss until thoroughly coated. If the sauce seems too thick, add in pasta water by the splash. Taste and adjust seasoning, then garnish with fresh herbs and chili flakes, if desired.