Abstract: A theoretical investigation is done to clarify the origin of the peak structure observed near the K-pp threshold in the in-flight He-3(K-, Lambda p)n reaction of the J-PARC E15 experiment, which could be a signal of the lightest kaonic nuclei, i.e., the (K) over bar NN (I = 1/2) state. For the investigation, we evaluate the Lambda p invariant mass spectrum assuming two possible scenarios to interpret the experimental peak. One assumes that the Lambda (1405) resonance is generated after the emission of an energetic neutron from the absorption of the initial K-, not forming a bound state with the remaining proton. This uncorrelated Lambda (1405)p system subsequently decays into the final Lambda p. The other scenario implies that, after the emission of the energetic neutron, a (K) over bar NN bound state is formed, decaying eventually into a Lambda p pair. Our results show that the experimental signal observed in the in-flight He-3(K-, Lambda p)n reaction at J-PARC is qualitatively well reproduced by the assumption that a (K) over bar NN bound state is generated in the reaction, definitely discarding the interpretation in terms of an uncorrelated Lambda (1405)p s tate.