  We derive the exact solutions for electrically charged black holes both in
the absence and presence of a cosmological constant in the gravity theory with
Lorentz violation induced by a background Kalb-Ramond (KR) field. The
corresponding thermodynamic properties are investigated. It is found that the
standard first law of thermodynamics and the Smarr formula remain valid for the
charged KR black holes. Nevertheless, the Lorentz-violating effect influences
their ranges of local thermodynamic stability and the first- and second-order
phase transition points. Furthermore, to examine the impact of Lorentz
violation on the motion of test particles in the spacetime, we analyze the
shadow and the innermost stable circular orbit (ISCO) of these black holes. Our
results reveal that both the shadow and ISCO radii exhibit a high sensitivity
to the Lorentz-violating parameter $\ell$, with a decrease observed as $\ell$
increases.
