We present a detailed numerical study of lepton-pair production via the Drell-Yan process above the Z-peak at the LHC. Our results consistently combine next-to-next-to-leading order QCD corrections and next-to-leading order electroweak effects, and include the leading photon-initiated processes using a recent extraction of the photon distribution function. We focus on the effects of electroweak corrections and of photon-photon scattering contributions, and demonstrate which kinematic distributions exhibit sensitivity to these corrections. We show that a combination of measurements allows them to be disentangled and separately determined.