We explore here the feasibility of using the recently introduced Lagrangian descriptors [A. M. Mancho et al., Commun. Nonlinear Sci. Numer. Simul. 18, 3530 (2013)1007-570410.1016/j.cnsns.2013.05.002] to unveil the usually rich dynamics taking place in the vibrations of molecular systems, especially if they are floppy. The principal novelty of our work is the inclusion of p norms in the definition of the descriptors in this kind of system, which greatly enhances their power to discern among the different structures existing in the phase space. As an illustration we use the LiCN molecule described by realistic potentials in two and three dimensions, which exhibits chaotic motion within a mixed phase space in the isomerization between the two wells corresponding to the linear isomer stable configurations, LiNC and LiCN. In particular, we pay special attention to the manifolds emerging from the unstable fixed point between the corresponding isomer wells, and also to the marginally stable structures around a parabolic point existing near the LiNC well.