Polar metals are rare because free carriers in metals screen electrostatic potential and eliminate internal dipoles. Degenerate doped ferroelectrics may create an approximate polar metallic phase. We use first-principles calculations to investigate $n$-doped ${\mathrm{LiNbO}}_{3}$-type oxides (${\mathrm{LiNbO}}_{3}$ as the prototype) and compare to widely studied perovskite oxides (${\mathrm{BaTiO}}_{3}$ as the prototype). In the rigid-band approximation, substantial polar displacements in $n$-doped ${\mathrm{LiNbO}}_{3}$ persist even at 0.3 $e/\mathrm{f}.\mathrm{u}.$ $(\ensuremath{\simeq}{10}^{21}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3})$, while polar displacements in $n$-doped ${\mathrm{BaTiO}}_{3}$ quickly get suppressed and completely vanish at 0.1 $e/\mathrm{f}.\mathrm{u}.$ Furthermore, in $n$-doped ${\mathrm{LiNbO}}_{3}$, Li-O displacements decay more slowly than Nb-O displacements, while in $n$-doped ${\mathrm{BaTiO}}_{3}$, Ba-O and Ti-O displacements decay approximately at the same rate. Supercell calculations that use oxygen vacancies as electron donors support the main results from the rigid-band approximation and provide more detailed charge distributions. Substantial cation displacements are observed throughout ${\mathrm{LiNbO}}_{3\ensuremath{-}\ensuremath{\delta}}\phantom{\rule{4pt}{0ex}}(\ensuremath{\delta}=4.2%)$, while cation displacements in ${\mathrm{BaTiO}}_{3\ensuremath{-}\ensuremath{\delta}}\phantom{\rule{4pt}{0ex}}(\ensuremath{\delta}=4.2%)$ are almost completely suppressed. We find that conduction electrons in ${\mathrm{LiNbO}}_{3\ensuremath{-}\ensuremath{\delta}}$ are not as uniformly distributed as in ${\mathrm{BaTiO}}_{3\ensuremath{-}\ensuremath{\delta}}$, implying that the rigid-band approximation should be used with caution in simulating electron-doped ${\mathrm{LiNbO}}_{3}$-type oxides. Our work shows that polar distortions and conduction can coexist in a wide range of electron concentration in $n$-doped ${\mathrm{LiNbO}}_{3}$, which is a practical approach to generating an approximate polar metallic phase. Combining doped ferroelectrics and doped semiconductors may create new functions for devices.