  Lu5Rh6Sn18 is one of the caged-type quasiskutterudite superconductors with
superconducting transition temperature Tc = 4.12 K. Here, we investigate the
effect of pressure on the superconductivity in Lu5Rh6Sn18 by combining high
pressure electrical transport, synchrotron x-ray diffraction (XRD) and chemical
doping. Application of high pressure can enhance both the metallicity and the
superconducting transition temperature in Lu5Rh6Sn18. Tc is found to show a
continuous increase reaching up to 5.50 K at 11.4 GPa. Our high pressure
synchrotron XRD measurements demonstrate the stability of the pristine crystal
structure up to 12.0 GPa. In contrast, Tc is suppressed after the substitution
of La ions in Lu sites, inducing negative chemical pressure. Our study provides
valuable insights into the improvement of superconductivity in caged compounds.
