  We consider topological defects for the $\lambda\phi^4$ theory in (1+1)
dimensions with a Lorentz-violating background.
  It has been shown, by M. Barreto et al. (2006) \cite{barreto2006defect}, one
cannot have original effects in (the leading order of) single scalar field
model.
  Here, we introduce a new Lorentz-violating term, next to leading order which
cannot be absorbed by any redefinition of the scalar field or coordinates.
  Our term is the lowest order term which leads to concrete effects on the kink
properties. We calculate the corrections to the kink shape and the
corresponding mass. Quantization of the kink is performed and the revised modes
are obtained. We find the bound and continuum states are affected due to this
Lorentz symmetry violation.
