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. 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 β 2, and for the coexistence candidates we take a few deformation regions bringing about minima of the energy within energy difference Δ 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 11 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 …