Supersymmetric models with bilinear $R$-parity violation can account for the observed neutrino masses and mixing parameters indicated by neutrino oscillation data. We consider minimal supergravity versions of bilinear $R$-parity violation where the lightest supersymmetric particle is a neutralino. This is unstable, with a large enough decay length to be detected at the CERN Large Hadron Collider. We analyze the Large Hadron Collider potential to determine the lightest supersymmetric particle properties, such as mass, lifetime and branching ratios, and discuss their relation to neutrino properties.