We study how the Lamb shift of a static atom is modified when a nearby planar body rotates rigidly about its normal while the atom is held at a fixed distance a. We derive a general formula for the shift in terms of the angularly Doppler-shifted reflection coefficients of the surface, valid for any axially symmetric planar material. Expanding the result to second order in the angular velocity , we identify two independent contributions associated with the orbital and spin components of the electromagnetic angular momentum. The orbital contribution, proportional to ()^2, reproduces locally the Lamb shift induced by a surface translating at the tangential velocity , whereas the spin contribution, proportional to (a)^2, originates from the rotational Doppler shift of the photon helicity and survives even on the rotation axis. We first illustrate the formalism using a graphene sheet and then apply it to finite-thickness Drude and plasma conductors and to doped semiconductors. Rotation enhances the Casimir-Polder interaction for graphene and metallic surfaces, whereas it weakens it for doped semiconductors, depending on whether the carrier plasma frequency reaches the near-field scale 1/a. Above a threshold angular velocity, the atomic level also acquires a finite linewidth, providing a spectroscopic signature of quantum friction. Furthermore, rotation induces a novel component of the Casimir-Polder force, which is perpendicular to both the standard normal attraction and the tangential quantum-friction force.