  We reanalyze the anomalous angular distribution of lepton pairs produced in a
pion-induced Drell-Yan process by taking into account the Glauber gluon effect
in the $k_T$ factorization theorem. Compared to the previous study, we adopt
the realistic parton distribution functions (PDFs) for a proton from the CTEQ
and for a pion from the xFitter, include the QCD evolutions of the strong
coupling and the PDFs, and integrate the differential cross section over the
kinematic regions for the NA10, E615 and COMPASS experiments. These
improvements then allow rigorous confrontations of theoretical results with the
data. It is shown that the lepton angular distribution and the violation of the
Lam-Tung relation measured in all the above experiments can be well
accommodated with a single Glauber phase. We illustrate the Glauber effect in
the geometric picture for a Drell-Yan process, and its distinction from the
conventional Boer-Mulders mechanism. The observables are pointed out, which can
be used to discriminate the two proposals, when data become more precise.
