We present ab initio calculations of the repulsive Coulomb barrier for several geometrically stable isomers of the BeC42-dianion. We describe how the deformation of certain isomers can account for the experimental Coulomb explosion images of the dianion. For the most stable linear isomer, C2-BeC2- we examined the electron tunneling process along the dissociation path to obtain C-2(-) plus BeC2-. We found the crossing point for autodetachment to be R-dis(c) = 3.25 Angstrom. R-dis is the bond length between 2 and BeC2-; at this point, the electron tunneling energy is equal to the maximum of the repulsive Coulomb barrier. In the framework of the Wenzel-Kramer-Brioullin theory, the electron-loss lifetime of the metastable C-2(-) Be C-2(-) dianion at the equilibrium geometry, R-dis = 1.64 Angstrom, was estimated to be about 5 ms. This lower limit is in agreement with the experimental results in which the BeC42- dianion has a lifetime much longer than 5 mus.