  BTZ black holes provide excellent frameworks for studying theories that are
at the interface of classical and quantum gravity. In this paper we couple the
Riemannian spacetime with the bumblebee field, in the background of massive
gravity, which produces the violation of spontaneous Lorentz symmetry. In this
setup we construct a large family of static vacuum BTZ black hole solutions. We
study the asymptotic behaviour of curvature invariants and show that our
resulting solutions describe asymptotically AdS (2+1)-dimensional BTZ black
holes with negative cosmological constant. For positive cosmological constant
they are de Sitter. Thermodynamics of these black holes is also analysed.
