  We analytically investigate the nonautonomous discrete rogue wave solutions
and their interaction in the generalized Ablowitz-Ladik-Hirota lattice with
variable coefficients, which possess complicated wave propagations in time and
are beyond the usual discrete rogue waves. When the amplitude of the tunnel
coupling coefficient between sites decreases, these nonautonomous discrete
rogue wave solutions become localized in time after they propagate over some
certain large critical values. Moreover, we find that the interaction between
nonautonomous discrete rogue waves is elastic. In particular, these results can
reduce to the usual discrete rogue wave solutions when the gain or loss term is
ignored.
