HTSC in the iron-based superconductors (Fe-SC) is one of the most active and challenging topics. Very recently some of us (F. Bernardini et al.) have reported SC in novel silicide LaFeSiH at Tc = 11 K. LaFeSiH is the first Fe-SC in without toxic elements. DFT calculations have revealed that the SC properties of this novel material are unconventional and cannot be explained by the electron-phonon mechanism in conventional BCS theory. Given the importance of understanding the similarities and differences in the pairing mechanism with other known Fe-based SC, we propose to use muon measurements on LaFeSiH to understand its unconventional SC. Since other musr facilities all over the world will also investigate LaFeSiH using their musr measurements, we therefore submit this proposal as a Rapid Access proposal to carry out the experiment as soon as possible for a fast high-impact publication.