To make the dressing, combine the avocado, ¾ cup water, ¼ cup olive oil, lemon juice and herbs in a blender. Season with ½ teaspoon salt and ¼ teaspoon pepper. Blend until very smooth, adding more water if needed to thin the dressing. Taste and adjust the seasoning. Set aside.
Bring a small pot of water to a boil. Add the eggs, reduce the heat and simmer for 11 minutes (less if you like a softer set yolk). Drain and run cold water over the eggs until they are cool to the touch. Peel the eggs and cut in half.
Toss the asparagus with the remaining 1 tablespoon olive oil and season lightly with salt and pepper. Grill the asparagus until bright green and crisp tender, about 8 minutes. At the same time, grill the sausages according to package instructions. Slice the grilled sausages into rounds.
To assemble the salad, separate the lettuce into individual leaves and arrange over a large platter. Arrange the grilled sausages, asparagus, hard-boiled eggs, sugar snap peas, radishes and cherry tomatoes over the lettuce and serve with the dressing on the side so people can dress it themselves.