  Many features of Bloch oscillations in one-dimensional quantum lattices with
a static force can be described by quasiclassical considerations for example by
means of the acceleration theorem, at least for Hermitian systems. Here the
quasiclassical approach is extended to non-Hermitian lattices, which are of
increasing interest. The analysis is based on a generalised non-Hermitian phase
space dynamics developed recently. Applications to a single-band tight-binding
system demonstrate that many features of the quantum dynamics can be understood
from this classical description qualitatively and even quantitatively. Two
non-Hermitian and $PT$-symmetric examples are studied, a Hatano-Nelson lattice
with real coupling constants and a system with purely imaginary couplings, both
for initially localised states in space or in momentum. It is shown that the
time-evolution of the norm of the wave packet and the expectation values of
position and momentum can be described in a classical picture.
