  In the present paper, a new class of black hole solutions is constructed in
even dimensional Lovelock Born-Infeld theory. These solutions are interesting
since, in some respects, they are closer to black hole solutions of an odd
dimensional Lovelock Chern-Simons theory than to the more usual black hole
solutions in even dimensions. This hybrid behavior arises when non-Einstein
base manifolds are considered. The entropies of these solutions have been
analyzed using Wald formalism. These metrics exhibit a quite non-trivial
behavior. Their entropies can change sign and can even be identically zero
depending on the geometry of the corresponding base manifolds. Therefore, the
request of thermodynamical stability constrains the geometry of the
non-Einstein base manifolds. It will be shown that some of these solutions can
support non-vanishing torsion. Eventually, the possibility to define a sort of
topological charge associated with torsion will be discussed.
