Soak the onion in cold water, 15 minutes. Meanwhile, hard-boil the eggs: Put the eggs in a saucepan and cover with cold water; bring to a boil and cook 2 minutes. Remove from the heat, cover and let sit 10 minutes. Remove with a slotted spoon to a bowl of ice water. Return the water to a boil and season with salt. Add the asparagus and cook 2 minutes. Drain and transfer to the ice water.
Make the dressing: Whisk the mustard, vinegar, lime zest and juice, and the sugar in a small bowl. Season with salt and pepper. Gradually whisk in the olive oil.
Drain the asparagus and chop. Toss the lettuce, asparagus, radishes, hearts of palm, cucumber, tomatoes, corn and avocados in a large bowl. Peel and chop the eggs and drain the onions, then add to the salad. Add the dressing and toss. Season with salt and pepper.