Cut potatoes in half and put in a large saucepan with eggs. Add water to cover. Bring to a boil, then reduce heat and simmer until potatoes are tender when pierced, about 12 minutes; transfer from pan with a slotted spoon and let cool. Transfer eggs to a bowl of ice water.
Meanwhile, set a steamer basket in a second large saucepan with an inch of water. Add green beans, cover, and bring water to a boil; reduce heat to medium and steam beans until tender-crisp, 6 to 8 minutes. Transfer beans to bowl of ice water.
Cut potatoes into chunks, then shell and quarter eggs.
Line a platter with watercress. Arrange rows of potatoes, green beans, tomatoes, olives, and eggs on top. Spoon cheese chunks from oil and arrange in another row. Stir lemon juice, salt, and pepper into oil left in cheese jar and spoon as much as you like over salad.