  In the context of novel solid electrolytes for solid-state batteries,
first-principles calculations are becoming increasingly more popular due to
their ability to reproduce and predict accurately the energy, structural, and
dynamical properties of fast-ion conductors. In order to accelerate the
discovery of new superionic conductors is convenient to establish meaningful
relations between ionic transport and simple materials descriptors. Recently,
several experimental studies on lithium fast-ion conductors have suggested a
correlation between lattice softness and enhanced ionic conductivity due to a
concomitant decrease in the activation energy for ion migration, $E_{a}$. In
this article, we employ extensive \emph{ab initio} molecular dynamics
simulations based on density functional theory to substantiate the links
between ionic transport and lattice dynamics in a number of structurally and
chemically distinct lithium superionic conductors. Our first-principles results
show no evidence for a direct and general correlation between $E_{a}$, or the
hopping attempt frequency, and lattice softness. However, we find that, in
agreement with recent observations, the pre-exponential factor of lithium
diffusivity, $D_{0}$, follows the Meyer-Neldel rule $\propto
\exp{\left(E_{a}/\langle \omega \rangle\right)}$, where $\langle \omega
\rangle$ represents an average phonon frequency. Hence, lattice softness can be
identified with enhanced lithium diffusivity but only within families of
superionic materials presenting very similar migration activation energies, due
to larger $D_{0}$. On the technical side, we show that neglection of
temperature effects in first-principles estimation of $E_{a}$ may lead to huge
inaccuracies of $\sim 10$\%. The limitations of zero-temperature harmonic
approaches in modeling of lithium-ion conductors are also illustrated.
