The Drell-Yan (DY) process stands for a unique probe to testing initial-state effects that is not accompanied with any final state interaction, either energy loss or absorption. Moreover, the measured DY dilepton pair mass allows to investigate different kinematical regions where coherence or non-coherent effects are expected only. For this purpose, we used the color dipole approach where for the first time the contribution of Z boson relevant at large dilepton invariant masses was included. We analyze several effects affecting the nuclear suppression, R_pA < 1, of dilepton pairs, such as nuclear shadowing (coherence effect) and effective energy loss due to initial state interactions (ISI) effects (non-coherent effects), which cause a strong suppression at large pT and forward rapidities and lead to the breakdown of the QCD factorisation. We perform predictions of the strong nuclear attenuation of produced dileptons due to the nuclear shadowing at small pT, forward rapidities and small dilepton masses. Besides, we also predict strong suppressions at large pT and large dilepton masses, where coherence effects are not expected, due to ISI effects that can be verified by the LHC experiments. Nuclear effects are studied also in terms of the correlation function in azimuthal angle between dilepton pair and a forward pion. We predict a characteristic double-peak structure of the correlation function arises for very forward pions and large-mass dilepton pairs.