In this talk I will use a long exact sequence (after recalling its construction) relating the Legendrian contact homology of the two ends of a Lagrangian cobordism and the singular homology of the cobordism to deduce some restrictions on the topology of this Lagrangian (when the negative end admits an augmentation). Considering a twisted version of this long exact sequence we will see that Lagrangian cobordisms from a Legendrian sphere admitting an augmentation to itself are smoothly trivial. I will recall all the basic definitions. This is a joint work with Georgios Dimitroglou Rizell, Paolo Ghiggini and Roman Golovko.