  We investigate ground states properties of Pb isotopes located between
neutron and proton drip-lines estimated by two-neutron (two-proton) separation
energies and Fermi energies within the deformed relativistic Hartree-Bogoliubov
theory in continuum (DRHBc). First, we report some candidates of nuclear shape
coexistence in the isotope chain. They are accessed by calculating total energy
as a function of the deformation parameter $\beta_2$, and for the coexistence
candidates we take a couple of the deformation region bringing about minima of
the energy within energy difference $\Delta E < $ 1 MeV. Second, the Pb
isotopes near neutron drip-lines are also investigated and compared to the
results by other nuclear mass models. We find out eleven neutron emitters,
$^{278 - 296, 300}$Pb, giving rise to the Pb peninsular near the neutron
drip-line. Finally, by exploiting the neutron and proton density we deduce the
neutron skin thickness (NST) of the Pb isotopes and compare to the available
experimental data. The recent data regarding the shape coexistence of
$^{184,186,188}$Pb and the NST of $^{208}$Pb are shown to be well matched with
the present results.
