In this paper, we apply Lagrangian descriptors to study the invariant manifolds that emerge from the top of two barriers existing in the LiCN⇌LiNC isomerization reaction. We demonstrate that the integration times must be large enough compared with the characteristic stability exponents of the periodic orbit under study. The invariant manifolds manifest as singularities in the Lagrangian descriptors. Furthermore, we develop an equivalent potential energy surface with 2 degrees of freedom, which reproduces with a great accuracy previous results [F. Revuelta, R. M. Benito, and F. Borondo, Phys. Rev. E 99, 032221 (2019)2470-004510.1103/PhysRevE.99.032221]. This surface allows the use of an adiabatic approximation to develop a more simplified potential energy with solely 1 degree of freedom. The reduced dimensional model is still able to qualitatively describe the results observed with the original 2-degrees-of-freedom potential energy landscape. Likewise, it is also used to study in a more simple manner the influence on the Lagrangian descriptors of a bifurcation, where some of the previous invariant manifolds emerge, even before it takes place.