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In the present paper, a new class of black hole solutions is constructed ineven dimensional Lovelock Born-Infeld theory. These solutions are interestingsince, in some respects, they are closer to black hole solutions of an odddimensional Lovelock Chern-Simons theory than to the more usual black holesolutions in even dimensions. This hybrid behavior arises when non-Einsteinbase manifolds are considered. The entropies of these solutions have beenanalyzed using Wald formalism. These metrics exhibit a quite non-trivialbehavior. Their entropies can change sign and can even be identically zerodepending on the geometry of the corresponding base manifolds. Therefore, therequest of thermodynamical stability constrains the geometry of thenon-Einstein base manifolds. It will be shown that some of these solutions cansupport non-vanishing torsion. Eventually, the possibility to define a sort oftopological charge associated with torsion will be discussed.

BTZ-like black holes in even dimensional Lovelock theories