Magnetic susceptibility, specific heat, and muon spin relaxation ($\ensuremath{\mu}\mathrm{SR}$) measurements have been performed on a synthesized three-dimensional sandglass-type lattice ${\mathrm{Tm}}_{3}{\mathrm{SbO}}_{7}$, where two inequivalent sets of non-Kramers ${\mathrm{Tm}}^{3+}$ ions (${\mathrm{Tm}}_{1}^{3+}$ ${\mathrm{Tm}}_{2}^{3+})$ show crystal electrical field effect at different...