Lumpy skin disease (LSD), caused by a virus within the Poxviridae family and Capripoxvirus genus, induces nodular skin lesions in cattle. This spreads through direct contact and insect vectors, significantly affecting global cattle farming. Despite the availability of vaccines, their efficacy is limited by poor prophylaxis and adverse effects. Our study aimed to identify the potential inhibitors targeting the LSDV-encoded DNA polymerase protein (gene LSDV039) for further investigation through comprehensive analysis and computational methods. Virtual screening revealed rhein and taxifolin as being potent binders among 380 phytocompounds, with respective affinities of −8.97 and −7.20 kcal/mol. Canagliflozin and tepotinib exhibited strong affinities (−9.86 and −8.86 kcal/mol) among 718 FDA-approved antiviral drugs. Simulating the molecular dynamics of canagliflozin, tepotinib, rhein, and taxifolin highlighted taxifolin’s superior stability and binding energy. Rhein displayed compactness in RMSD and RMSF, but fluctuated in Rg and SASA, while canagliflozin demonstrated stability compared to tepotinib. This study highlights the promising potential of using repurposed drugs and phytocompounds as potential LSD therapeutics. However, extensive validation through in vitro and in vivo testing and clinical trials is crucial for their practical application.