  In this paper we present a new family of wormhole geometries in Lovelock
theories with a unique vacuum, and study their stability under scalar field
perturbations. As the solutions already known in the literature for
Chern-Simons gravity on AdS, the new wormholes are characterized by a single
integration constant $\rho_{0}$, that parameterizes the contribution to the
mass coming from each boundary, which cancel each other, leading to a new
example of "mass without mass". The stability of these new configurations, as
well as other previously constructed in the literature is explored under scalar
field perturbations. The stability is ensured provided the mass of the scalar
perturbation is above a deformed Breitenlohner-Freedman bound which is
sensitive to the value of $\rho_{0}$.
