  The electric conductivity, $\sigma_{\rm el}$, is a fundamental transport
coefficient of QCD matter that can be related to the zero-energy limit of the
electromagnetic (EM) spectral function at vanishing 3-momentum in the medium.
The EM spectral function is also the central quantity to describe the thermal
emission rates and pertinent spectra of photon and dilepton radiation in
heavy-ion collisions. Employing a model for dilepton rates that combines
hadronic many-body theory with nonperturbative QGP emission constrained by
lattice-QCD which describes existing dilepton measurements in heavy-ion
collisions, we investigate the sensitivity of low-mass dilepton spectra in
Pb-Pb collisions at the LHC to $\sigma_{\rm el}$. In particular, we disentangle
the contributions from QGP and hadronic emission, and identify signatures that
can help to extract $\sigma_{\rm el}$ from high-precision experimental data
expected to be attainable with future detector systems at the LHC.
