Scrub potatoes and put in a 5- to 6-quart pan. Add 2 quarts water. Cover pan and bring to a boil over high heat, then reduce heat and simmer until potatoes are tender when pierced, 10 to 15 minutes. With a slotted spoon, lift potatoes out and let cool.
Meanwhile, rinse asparagus and peas. Snap off tough stem ends of asparagus. Remove strings from peas. Return water used for potatoes to a boil again over high heat. Add asparagus and cook just until barely tender when pierced, 3 to 5 minutes. Lift out with tongs and immerse in a bowl filled with ice water. When cool, drain. Add peas to the same boiling water and cook just until bright green, about 2 minutes. Drain and immerse in ice water until cool; drain again.
Add about 3 quarts water and the lemon juice, olive oil, and salt to the pan (no need to wash). Cover and bring to a boil over high heat. Meanwhile, rinse artichokes. Trim about 1 inch off tops and discard. With scissors, trim remaining thorny tips off outer leaves. Trim off stems. Cut in half lengthwise. Immerse artichokes in the boiling water and cover. When water returns to a boil, reduce heat and simmer, covered, until artichokes are tender when pierced in base, about 20 minutes. Drain and let cool.
Arrange potatoes, asparagus, peas, artichokes, radishes, shrimp, and eggs in a basket or on a platter. Serve with aioli.