Bring a large saucepan of salted water to a boil and have ready a large bowl of ice and cold water. Trim haricots verts to 3-inch lengths and blanch in boiling water 2 minutes. Transfer beans with a slotted spoon to ice water to stop cooking and drain in a colander. In same boiling water cook onions 5 minutes and with slotted spoon transfer to colander to drain. In same boiling water simmer potatoes 7 minutes, or until tender, and drain in colander. Peel and halve onions and transfer to a bowl. Vegetables may be prepared up to this point 1 day ahead, cooled completely, and chilled in a sealable plastic bag.
Halve shiitakes if large. In a large heavy skillet heat butter over moderate heat until foam subsides and cook shiitakes with salt to taste, stirring occasionally, 2 minutes, or until just tender. Add peas and cook 2 minutes, or until bright green. Add beans, onions, and potatoes and cook, stirring occasionally, until just heated through. Stir in chives and season with salt and pepper and lemon zest and juice.