Add pancetta to a large room temperature pan or skillet. Place over medium-low heat and allow time to render and crisp, shaking every so often, about 10-12 minutes. Use a slotted spoon to transfer the pancetta to a plate (without removing the fat from the pan or skillet) and set aside.
Increase heat to high. Add celery in a single layer, working in batches, if needed, and cook for 3-4 minutes on each side (it should absorb some of the fat, gain color, and begin to soften), then remove from the pan and set aside.
Lower heat to medium, add shallots, and cook until translucent and fragrant. Return celery to the pan, increase heat to high, and add white wine. When more than half of the wine has reduced, add chicken stock, making sure the celery is as submerged as possible. Cover with a lid and simmer for 45 minutes, until celery is tender but not mushy.
Remove the lid and add beans and pancetta. Continue to cook until the liquid is almost entirely reduced. Stir in butter and lemon juice and top with a drizzle of olive oil and fresh dill. Taste, and, if needed, add salt.