  We find novel site-dependent Lax operators in terms of which we demonstrate
exact solvability of a dissipatively driven XYZ spin-1/2 chain in the Zeno
limit of strong dissipation, with jump operators polarizing the boundary spins
in arbitrary directions. We write the corresponding nonequilibrium steady state
using an inhomogeneous MPA, where the constituent matrices satisfy a simple set
of linear recurrence relations. Although these matrices can be embedded into an
infinite-dimensional auxiliary space, we have verified that they cannot be
simultaneously put into a tridiagonal form, not even in the case of axially
symmetric (XXZ) bulk interactions and general nonlongitudinal boundary
dissipation. We expect our results to have further fundamental applications for
the construction of nonlocal integrals of motion for the open XYZ model with
arbitrary boundary fields, or the eight-vertex model.
