We discuss the Drell-Yan production of dileptons at high energies in the forward rapidity region of proton-proton collisions in a hybrid high-energy approach. This approach uses unintegrated gluon distributions in one proton and collinear quark/antiquark distributions in the second proton. We compute various distributions for the case of low-mass dilepton production and compare to the LHCb and ATLAS experimental data on dilepton mass distributions. In distinction to dipole approaches, we include four DrellYan structure functions as well as cuts at the level of lepton kinematics. The impact of the interference structure functions is rather small for typical experimental cuts. We find that both side contributions (gq/q¯ and q/qg¯ ) have to be included even for the LHCb rapidity coverage which is in contradiction with what is usually done in the dipole approach. We present results for different unintegrated gluon distributions from the literature. Some of them include saturation effects, but we see no clear hints of saturation even at small Mll.