  The effects of dark matter spike in the vicinity of the supermassive black
hole, located at the center of M87 (the Virgo A galaxy), are investigated
within the framework of the so-called Bumblebee Gravity. Our primary aim is to
determine whether the background of spontaneous Lorentz symmetry breaking has a
significant effect on the horizon, ergo-region, and shadow of the Kerr
Bumblebee black hole in the spike region. For this purpose, we first
incorporate the dark matter distribution in a Lorentz-violating spherically
symmetric space-time as a component of the energy-momentum tensors in the
Einstein field equations. This leads to a space-time metric for a Schwarzschild
Bumblebee black hole with a dark matter distribution in the spike region and
beyond. Subsequently, this solution is generalized to a Kerr Bumblebee black
hole through the use of the Newman-Janis-Azreg-A\"inou algorithm. Then,
according to the available observational data for the dark matter spike density
and radius, and the Schwarzschild radius of the supermassive black hole in
Virgo A galaxy, we examine the shapes of shadow and demonstrate the influence
of the spin parameter $a$, the Lorentz-violating parameter $\ell$ and the
corresponding dark matter halo parameters $\rho_{0}$ and $r_{0}$ on the
deformation and size of the shadow.
