  In this paper, we investigate the action growth in various backgrounds in
Einstein-Maxwell-Dilaton theory. We calculate the full time evolution of action
growth in AdS dilaton black hole and find it approaches the late time bound
from above. We investigate the black hole which is asymptotically Lifshitz and
obtain its late-time and full time behavior. We find the violation of Lloyd
bound in late time limit and show the full time behavior exhibiting some new
features for z sufficiently large.
