Hexagonal LuFeO$_3$ has drawn a lot of research attention due to its contentious room-temperature multiferroicity. Due to the unstability of hexagonal phase in the bulk form, most experimental studies focused on LuFeO$_3$ thin films which can be stabilized by strain using proper substrates. Here we report on the hexagonal phase stabilization, magnetism, and magnetoelectric coupling of bulk LuFeO$_3$ by partial Sc-substitution of Lu. First, our first-principles calculations show that the hexagonal structure can be stabilized by partial Sc substitution, while the multiferroic properties including the noncollinear magnetic order and geometric ferroelectricity remain robustly unaffected. Therefore, Lu$_{1-x}$Sc$_x$FeO$_3$ can act as a platform to check the multiferroicity of LuFeO$_3$ and related materials in the bulk form. Second, the magnetic characterizations on bulk Lu$_{1-x}$Sc$_x$FeO$_3$ demonstrate a magnetic anomaly (probable antiferromagnetic ordering) above room temperature, $sim425-445$ K, followed by magnetic transitions in low temperatures ($sim167-172$ K). In addition, a magnetoelectric response is observed in the low temperature region. Our study provides useful information on the multiferroic physics of hexagonal $R$FeO$_3$ and related systems.
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