  We study dynamical properties of dissipative XYZ Heisenberg lattices where
anisotropic spin-spin coupling competes with local incoherent spin flip
processes. In particular, we explore a region of the parameter space where
dissipative magnetic phase transitions for the steady state have been recently
predicted by mean-field theories and exact numerical methods. We investigate
the asymptotic decay rate towards the steady state both in 1D (up to the
thermodynamical limit) and in finite-size 2D lattices, showing that critical
dynamics does not occur in 1D, but it can emerge in 2D. We also analyze the
behavior of individual homodyne quantum trajectories, which well reveal the
nature of the transition.
