Bring a large pot of lightly salted water to a boil. Cook bucatini in the boiling water, stirring occasionally, until tender yet firm to the bite, about 11 minutes.

Meanwhile, heat a nonstick pan over medium-low heat. Add pancetta and cook until tender and the fat has rendered. Remove from heat.

Ladle 1 cup pasta cooking water into a bowl; set aside.

Puree avocado in a bowl using a hand blender. Add 1/4 cup Pecorino Romano cheese, egg yolks, 2 teaspoons black pepper, and lemon juice. Stir well until sauce is creamy.

Use spaghetti tongs to add the pasta directly from the water to the pan with the pancetta, allowing a bit of pasta water to help thin the sauce. Toss the pasta in the skillet to coat the pasta with the pancetta. Add avocado sauce to the pasta, stirring constantly. Mix in reserved pasta water if necessary.