The magnetic and structural properties of the recently discovered
pnictogen/chalcogen-free superconductor LaFeSiH (Tc≃10~K) have been
investigated by 57Fe synchrotron M{\"o}ssbauer source (SMS) spectroscopy,
x-ray and neutron powder diffraction and 29Si nuclear magnetic resonance
spectroscopy (NMR). No sign of long range magnetic order or local moments has
been detected in any of the measurements and LaFeSiH remains tetragonal down to
2 K. The activated temperature dependence of both the NMR Knight shift and the
relaxation rate 1/T1 is analogous to that observed in strongly overdoped
Fe-based superconductors. These results, together with the
temperature-independent NMR linewidth, show that LaFeSiH is an homogeneous
metal, far from any magnetic or nematic instability, and with similar Fermi
surface properties as strongly overdoped iron pnictides. This raises the
prospect of enhancing the Tc of LaFeSiH by reducing its carrier
concentration through appropriate chemical substitutions. Additional SMS
spectroscopy measurements under hydrostatic pressure up to 18.8~GPa found no
measurable hyperfine field