Hard boil the eggs, peel when cool enough to handle, and set aside. You can do this well in advance if you like.
Preheat grill to high (about 400-500°F). Place the salmon skin-side down on a double layer of aluminum foil. Sprinkle generously with salt and pepper and lay the lemon slices over the flesh. Grill salmon until done to your liking, about 8-10 minutes for just barely opaque in the center, depending on thickness. Place salmon in the center of a large serving platter with the lemon slices off to the side.
Rub asparagus with two tablespoons of the olive oil, sprinkle with salt and pepper, and grill until nicely charred, 2-3 minutes per side, flipping once. Add asparagus to platter.
Trim tough ends from green beans and boil or steam until crisp-tender. If you like, plunge into a large bowl of ice water to stop cooking and preserve bright green color.
In a small bowl, combine the remaining olive oil, vinegar, mustard and plenty of salt and pepper. Whisk to emulsify.
Add arugula and olives to platter. Halve hard-boiled eggs lengthwise and add them to the platter too.
Sprinkle everything with a bit of flaky sea salt. Serve with dressing.