  We investigate the steady-state phases of the dissipative spin-1/2
$J_1$-$J_2$ XYZ model on a two-dimensional square lattice. We show the
next-nearest-neighboring interaction plays a crucial role in determining the
steady-state properties. By means of the Gutzwiller mean-field factorization,
we find the emergence of antiferromag-netic steady-state phases. The existence
of such antiferromagnetic steady-state phases in thermodynamic limit is
confirmed by the cluster mean-field analysis. Moreover, we find the evidence of
the limit cycle phase through the largest quantum Lyapunov exponent in small
cluster, and check the stability of the oscillation by calculating the averaged
oscillation amplitude up to $4\times4$ cluster mean-field approximation.
