  At the LHC, dileptonic events may turn up new physics interacting with quarks
and leptons. The poster child for this scenario is a resonant $Z'$, much
anticipated in $\ell^+ \ell^-$ invariant mass spectra. However, angular spectra
of dileptons may play an equal or stronger role in discovering a non-resonant
species. This paper avails of their LHC measurements to corner the couplings
and masses of leptoquarks (LQs), that can mediate $q \bar{q} \rightarrow \ell^+
\ell^-$ in the $t$-channel and dramatically alter Standard Model angular
spectra. Also derived are constraints from alterations to $m_{\ell \ell}$
distributions. These dilepton probes, exploiting the high rates and small
uncertainties of the Drell-Yan process, rival or outdo dedicated LHC searches
for LQs in single and pair production modes. The couplings of LQs with
electronic interactions are best bound today by low-energy measurements of
atomic parity violation, but can be probed better by $\ell^+ \ell^-$
measurements in the high luminosity runs of the LHC, with the angular spectra
leading the way. This work also advocates the experimental presentation of
boost-invariant angular asymmetries that vanish in the SM.
