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We employ synchrotron-based near-field infrared spectroscopy to image the phononic properties of ferroelectric domain walls in hexagonal (h) Lu0.6Sc0.4FeO3, and we compare our findings with a detailed symmetry analysis, lattice dynamics calculations, and prior models of domain-wall structure. Rather than metallic and atomically thin as observed in the rare-earth manganites, ferroelectric walls in h-Lu0.6Sc0.4FeO3 are broad and semiconducting, a finding that we attribute to the presence of an A-site substitution-induced intermediate phase that reduces strain and renders the interior of the domain wall nonpolar. Mixed Lu/Sc occupation on the A site also provides compositional heterogeneity over micron-sized length scales, and we leverage the fact that Lu and Sc cluster in different ratios to demonstrate that the spectral characteristics at the wall are robust even in different compositional regimes. This work opens the door to broadband imaging of physical and chemical heterogeneity in ferroics and represents an important step toward revealing the rich properties of these flexible defect states.