  We present a new family of exact black hole configurations which is a
solution to a generalized Einstein-Dilaton-Maxwell setup. These solutions are
asymptotically Lifshitz for any dynamical critical exponent $z\geq 1$. The
existence of a non-trivial scalar field is a direct consequence of breaking the
spacetime isotropic scaling symmetry. This black hole family accepts various
interesting limits that link it to well-known solutions in both the isotropic
and anisotropic cases. Furthermore, we show that for a certain parameter
region, the anisotropic scalarized field configuration is thermodynamically
preferred. Hence, our solution provides an analytical example that black hole
spontaneous scalarization can emerge as an effect of asymmetric scaling between
space and time.
