Coarsely mash the avocados in a bowl with the lemon zest and juice, 1/4 teaspoon salt and pepper to taste. Spread the mash evenly onto the toasts.
Melt the butter in a medium nonstick skillet over medium-low heat. Add the cream cheese, eggs and 1/4 teaspoon salt and cook, stirring constantly with a rubber spatula, until the mixture is just set with small, creamy curds, about 5 minutes. Spoon the eggs onto the toasts and top with the radishes and chives. Sprinkle with salt.