  We explore the ultra-relativistic limit of a class of four dimensional
gravity theories, known as Lovelock-Cartan gravities, in the first order
formalism. First, we review the well known limit of the Einstein-Hilbert
action. A very useful scale symmetry involving the vierbeins and the boost
connection is presented. Moreover, we explore the field equations in order to
find formal solutions. Some remarkable results are obtained: Riemann and
Weitzenb\"ock like manifolds are discussed; Birkhoff's theorem is verified for
the torsionless case; an explicit solution with non-trivial geometry is
discussed; A quite general solution in the presence of matter is obtained.
Latter, we consider the ultra-relativistic limit of the more general
Lovelock-Cartan gravity. The previously scale symmetry is also discussed. The
field equations are studied in vacuum and in the presence of matter. In
comparison with the Einstein-Hilbert case, a few relevant results are found:
Birkhoff's theorem is also verified for the torsionless case; A quite general
solution in the presence of matter is obtained. This solution generalizes the
previous case; Riemann and Weitzenb\"ock like manifolds are derived in the same
lines of the Einstein-Hilbert case.
