Cook the spaghetti according to package directions until al dente. Drain and reserve ½ cup of the pasta water.
Meanwhile, cook the bacon in a wide, deep skillet over medium heat until crispy, turning occasionally. Remove to a paper towel to drain and cool. Crumble the bacon and reserve.
Season the chicken strips lightly with salt and black pepper. Add to the pan where the bacon cooked and cook over medium until chicken is cooked through, 5-6 minutes. Add the garlic and cook for 1 more minute.
Add the pasta and the reserved bacon to the pan and mix to combine. Reduce the heat to medium low.
In a separate bowl, whisk the eggs and Parmesan cheese together, along with a pinch of black pepper.
Add the egg mixture to the pasta and chicken mixture. Stir well, quickly and constantly, to coat the noodles (and to avoid scrambling the eggs.) Add a splash of reserved pasta water, as needed, to help the sauce adhere to the noodles.
Cook for 3-4 minutes to warm through then top the dish with lemon zest and serve immediately, with extra Parmesan cheese and black pepper if desired.