  Ultrasound velocity measurements were performed on a single crystal of
spin-frustrated ferrite spinel ZnFe$_2$O$_4$ from 300 K down to 2 K. In this
cubic crystal, all the symmetrically-independent elastic moduli exhibit
softening with a characteristic minimum with decreasing temperature below
$\sim$100 K. This elastic anomaly suggests a coupling between dynamical lattice
deformations and molecular-spin excitations. In contrast, the elastic
anomalies, normally driven by the magnetostructural phase transition and its
precursor, are absent in ZnFe$_2$O$_4$, suggesting that the spin-lattice
coupling cannot play a role in relieving frustration within this compound. The
present study infers that, for ZnFe$_2$O$_4$, the dynamical molecular-spin
state evolves at low temperatures without undergoing precursor spin-lattice
fluctuations and spin-lattice ordering. It is expected that ZnFe$_2$O$_4$
provides the unique dynamical spin-lattice liquid-like system, where not only
the spin molecules but also the cubic lattice fluctuate spatially and
temporally.
