HERBED AIOLI: Combine 2 tbsp water, egg yolks, lemon juice, and garlic in medium metal bowl; whisk to blend. Place bowl over saucepan of simmering water (do not allow bottom of bowl to touch water). Whisk until mixture thickens and thermometer registers 160°, 5-6 minutes. Remove from over water. Cool 10 minutes.
Gradually whisk olive oil into aioli base, then 2 Tbsp water. Whisk in chives and parsley. Season aioli to taste with salt and freshly ground black pepper. DO AHEAD: Can be made 1 day ahead. Cover and chill. Bring aioli to room temperature and whisk before using.
DRESSING: Whisk oil and lemon juice in medium bowl to blend. Season dressing to taste with salt and pepper.
ASSEMBLY: Combine greens and radicchio in large bowl. Add dressing and toss to coat. Arrange greens mixture on large platter or divide among plates. Top with fish and egg. Drizzle some aioli over. Serve, passing remaining aioli alongside.
