We explore the selective electrocatalytic hydrogenation of lignin monomers to methoxylated chemicals, of particular interest, when powered by renewable electricity. Prior studies, while advancing the field rapidly, have so far lacked the needed selectivity: when hydrogenating lignin-derived methoxylated monomers to methoxylated cyclohexanes, the desired methoxy group (-OCH3) has also been reduced. The ternary PtRhAu electrocatalysts developed herein selectively hydrogenate lignin monomers to methoxylated cyclohexanes - molecules with uses in pharmaceutics. Using X-ray absorption spectroscopy and in situ Raman spectroscopy, we find that Rh and Au modulate the electronic structure of Pt and that this modulating steers intermediate energetics on the electrocatalyst surface to facilitate the hydrogenation of lignin monomers and suppress C-OCH3 bond cleavage. As a result, PtRhAu electrocatalysts achieve a record 58% faradaic efficiency (FE) toward 2-methoxycyclohexanol from the lignin monomer guaiacol at 200 mA cm-2, representing a 1.9× advance in FE and a 4× increase in partial current density compared to the highest productivity prior reports. We demonstrate an integrated lignin biorefinery where wood-derived lignin monomers are selectively hydrogenated and funneled to methoxylated 2-methoxy-4-propylcyclohexanol using PtRhAu electrocatalysts. This work offers an opportunity for the sustainable electrocatalytic synthesis of methoxylated pharmaceuticals from renewable biomass.