Unraveling the interplay of spins, lattice, and pressure in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>LuFe</mml:mi><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math>:

The multiferroic $\mathrm{LuFe}{\mathrm{O}}_{3}$ unusually shows a magnetic order that causes ferroelectricity up to a rather high temperature of 610 K indicating very strong magnetoelectric coupling. We present the inelastic neutron-scattering (INS) measurements and ab initio density-functional theory-based simulation studies of $\mathrm{LuFe}{\mathrm{O}}_{3}$ to elucidate the lattice and spin dynamics. We have analyzed the phonon density of states and magnon density of states from INS measurements and compared them with the results of our simulations. We identified that specific iron- and oxygen-dominated optical phonon modes largely govern the spin-lattice coupling. Besides these, our simulations also reveal that the computed acoustic phonon branches are sensitive to the underlying magnetic structure, inferring strong magnetoelastic coupling. The signature of magnetoelastic coupling is also observed in the reported measurement of lattice parameters showing significant change across the magnetic transition ${T}_{\mathrm{N}}\ensuremath{\sim}610$ K. We further investigated the pressure dependent high-spin to low-spin transition and its influence on lattice dynamics. We have identified the critical structural parameters governing the spin phase transition.