quantum electrodynamics - Why does the Lamb shift only affect s-states?

The shift is due to interactions between atomic electrons and vacuum state fluctuations, so I would think that there would be an associated energy shift for all states, and not just s-states.

Also, is there any physical relationship between the Lamb shift and the Darwin correction for hydrogen? The explanation for the Darwin term is usually "Zitterbewegung", which is often in turn justified by the same processes contributing to the Lamb shift.