  We demonstrate that small but finite ferroelectric polarization ($\sim$0.01
$\mu$C/cm$^2$) emerges in orthorhombic LuFeO$_3$ ($Pnma$) at $T_N$ ($\sim$600
K) because of commensurate (k = 0) and collinear magnetic structure. The
synchrotron x-ray and neutron diffraction data suggest that the polarization
could originate from enhanced bond covalency together with subtle contribution
from lattice. The theoretical calculations indicate enhancement of bond
covalency as well as the possibility of structural transition to the polar
$Pna2_1$ phase below $T_N$. The $Pna2_1$ phase, in fact, is found to be
energetically favorable below $T_N$ in orthorhombic LuFeO$_3$ ($albeit$ with
very small energy difference) than in isostructural and nonferroelectric
LaFeO$_3$ or NdFeO$_3$. Application of electric field induces finite
piezostriction in LuFeO$_3$ via electrostriction resulting in clear domain
contrast images in piezoresponse force microscopy.
