Neutral current Drell-Yan (DY) lepton-pair production is considered to study Z-boson quark couplings. Using the open-source fit platform xFitter, we investigate the impact of high-statistics measurements of the neutral current DY (NCDY) forward- backward asymmetry AFB near the weak boson mass scale in the present and forthcom- ing stages of the Large Hadron Collider (LHC). Besides recovering earlier results on the AFB sensitivity to parton distribution functions, we analyze the precision determination of Z-boson couplings to left-handed and right-handed u-quarks and d-quarks, and explore Beyond-Standard-Model contributions using the Standard Model Effective Field Theory (SMEFT) framework. We perform a sensitivity study and comment on the role of the AFB asymmetry for the electroweak SMEFT fit and precision Z-boson physics at the LHC and high-luminosity HL-LHC.