Cook spaghetti in salted boiling water until slightly underdone (about 6 to 7 minutes). Reserve 1 cup of pasta water and then drain.
In a large skillet, heat olive oil and 2 tablespoons of butter over medium heat. Add garlic and anchovy paste, sauté until garlic is golden.
Increase heat to medium-high, add white wine and clam juice. If using fresh clams, add them now, cover and simmer for 7-10 minutes. Discard any unopened clams.
Reduce heat to low, stir in lemon juice and zest. If using canned clams, add them now. Add the cooked spaghetti, tossing it in the sauce, adding reserved pasta water if needed.
Let it simmer for 2-3 minutes, then remove from heat and stir in remaining 2 tablespoons of butter until melted. Season with salt and pepper.
Garnish with chopped parsley and serve immediately.