  When the next galactic core-collapse supernova occurs, we must be ready to
obtain as much information as possible. Although many present and future
detectors are well equipped to detect $\overline{\nu}_{\mathrm{e}}$ and $\nu_x$
neutrinos, the detection of the $\nu_{\mathrm{e}}$ species presents the biggest
challenges. We assess the impact that a 1 ktonne lead-based detector, such as
HALO-1kT, can have in constraining electron neutrino time-integrated fluxes.
The study involves the detector taken alone as well as when combined with
massive $\overline{\nu}_{\mathrm{e}}$-sensitive detectors such as
Super-Kamiokande and JUNO. We find that HALO-1kT alone is not able to strongly
constrain the emission parameters. When combined with other detectors, however,
the orthogonal information might be helpful in improving the $\nu_{\mathrm{e}}$
total emitted energy and mean energy accuracy, up to about $50\%$, if no other
$\nu_{\mathrm{e}}$-sensitive channel is implemented. A discussion on the
reconstruction of $\overline{\nu}_{\mathrm{e}}$ and $\nu_x$ species, as well as
the total emitted energy, is also presented.
