I see here that there are three contributions to the Lamb shift, from vacuum polarization (-27 MHz), from electron mass renormalization(+1017 MHz), and from the anomalous magnetic moment (+68 MHz).
These look to be the renormalized 2-point photon propagator, the renormalized 2-point Dirac spinor propagator, and the renormalized 3-point VEV for two Dirac spinors and a photon.
In my experience, derivations of the Lamb shift are somewhat long and messy. If we take the derivation of some set of renormalized n-point VEVs for granted, is the derivation of the Lamb shift from that point forward relatively short and clean?
Although someone might feel like deriving this relation (or showing that there is no such relation) in a few lines as an Answer, and I would be interested if it can be done briefly and convincingly, I would probably prefer a reference to somewhere that derives the Lamb shift in terms of the renormalized VEVs. Failing that, a reference to your favorite derivation of the Lamb shift, either in Comments or as an Answer, would be Useful to me, even if it doesn't conform to the prejudices you can see on display above.
Finally, if the Question seems ill-put, as I suspect it might be, please feel very free to tell me so. Wanna learn.