Neutron powder diffraction (NPD) study of textit{Ln}MnSbO (textit{Ln }$=$ La or Ce) reveals differences between the magnetic ground state of the two compounds due to the strong Ce-Mn coupling compared to La-Mn. The two compounds adopt the textit{P4/nmm} space group down to 2 K and whereas magnetization measurements do not show obvious anomaly at high temperatures, NPD reveals a C-type antiferromagnetic (AFM) order below $T_{mathrm{N}} = 255 $ K for LaMnSbO and 240 K for CeMnSbO. While the magnetic structure of LaMnSbO is preserved to base temperature, a sharp transition at $T_{mathrm{SR}} = 4.5 $K is observed in CeMnSbO due to a spin-reorientation (SR) transition of the Mn$^{mathrm{2+}}$ magnetic moments from pointing along the $c$-axis to the textit{ab}-plane. The SR transition in CeMnSbO is accompanied by a simultaneous long-range AFM ordering of the Ce moments which indicates that the Mn SR transition is driven by the Ce-Mn coupling. The ordered moments are found to be somewhat smaller than those expected for Mn$^{mathrm{2+}}$ ($S = 5/2$) in insulators, but large enough to suggest that these compounds belong to the class of local-moment antiferromagnets. The lower $T_{mathrm{Nthinspace }}$ found in these two compounds compared to the As-based counterparts ($T_{mathrm{N}} = 317$ for LaMnAsO, $T_{mathrm{N}} = 347$ K for CeMnAsO) indicates that the Mn-$Pn$ ($Pn=$ As or Sb) hybridization that mediates the superexchange Mn-$Pn$-Mn coupling is weaker for the Sb-based compounds.
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