The LHC-forward experiment (LHCf), located at the Large Hadron Collider (LHC), is designed to measure the production cross section of neutral particles in the pseudorapidity region above 8.4, up to zero-degree. The measurement of the very-forward particle production rates at the highest energy available at an accelerator will provides fundamental informations for the tuning of the phenomenological hadronic interaction models used in the simulation of air-showers induced by ultra-high-energy cosmic rays in the Earth atmosphere. The experiment consists of two small independent detectors placed 140 metres away from the ATLAS interaction point (IP1), on opposite sides. Each detector is made of two sampling and position sensitive calorimeters. This contribution will firstly highlight the Run II physics results of LHCf in proton-proton collisions at 13 TeV: the photon and neutron production spectra will be presented and compared with the predictions of several hadronic interaction models commonly used in air-shower simulations. Furthermore, the advantages of the ATLAS-LHCf combined analysis will be discussed and the energy spectrum of very-forward photons produced in diffractive collisions (tagged by ATLAS central detectors) will be shown together with models predictions. Later, a report of the successful LHCf data taking during its dedicated run with proton-proton collisions at 13.6 TeV performed on September 2022 will be presented. Finally, the physics motivation of the foreseen operation with proton-oxygen collisions at the LHC will be illustrated.