Put the eggs and turnips in a saucepan, cover with water and bring to a boil. Remove from the heat and let stand, covered, 10 minutes. Remove the eggs but keep the turnips in the hot water, covered, until tender, 2 to 3 more minutes. Peel the eggs and cut into quarters.
Drain the turnips, then return to the warm pan and toss with the butter (turn on the heat to melt the butter if needed). Add the tarragon, chives, olive oil and lemon juice and toss.
Toss the endive, lettuce, escarole, celery and beans in a large
bowl and season with salt and pepper. Add the eggs and turnip mixture and gently toss again.