  One considers a planar Maxwell-Chern-Simons electrodynamics in the presence
of a purely spacelike Lorentz-violating background. Once the Dirac sector is
properly introduced and coupled to the scalar and the gauge fields, the
electron-electron interaction is evaluated as the Fourier transform of the
Moller scattering amplitude (derived in the non-relativistic limit). The
associated Fourier integrations can not be exactly carried out, but an
algebraic solution for the interaction potential is obtained in leading order
in (v/s)^2. It is then observed that the scalar potential presents a
logarithmic attractive (repulsive) behavior near (far from) the origin.
Concerning the gauge potential, it is composed of the pure MCS interaction
corrected by background contributions, also responsible for its anisotropic
character. It is also verified that such corrections may turn the gauge
potential attractive for some parameter values. Such attractiveness remains
even in the presence of the centrifugal barrier and gauge invariant A.A term,
which constitutes a condition compatible with the formation of Cooper pairs.
