We present structural properties at different temperatures and high-pressure (HP) of La3Rh4Sn13 which is one of the interesting systems in the Remika phase RE3Rh4Sn13 (RE=Sr, Ca, La, Pr, Ce) quasi-skutterudite series using synchrotron diffraction. Data at ambient conditions revealed the presence of several weak reflections, which could be accounted only with a superlattice I* structure (I4132) with lattice parameter a~19.457 Å. However, above 350 K, a complete suppression of the weak superlattice reflections of the I* structure is observed. Data at higher temperatures is found to be well described by the I structure (Pm-3n) having half the lattice parameter compared to the I* structure. HP-XRPD at ambient temperature showed that pressures greater than 7.5 GPa result in similar suppression of the weak I* superlattice reflections. Data at higher pressures is found to be well described by the I structure (Pm-3n), similar to the high-temperature phase. HP Raman measurements demonstrated changes that seem to be consistent with a locally more ordered structure as in the case of the I*→I transition. Our findings on La3Rh4Sn13 open up new avenues to study unexplored HP phenomena, especially the superconductivity in these Remika phase quasi-skutterudites.