In superconductors, the inversion symmetry of the crystallographic structure plays a central role in the formation of the Cooper pairs. The intermetallic compounds La7Pd3 and La7Ru3 are noncentrosymmetric (NCS) and centrosymmetric (CS), respectively. We propose to study the superconducting properties of La7Pd3 and La7Ru3 using muons as a microscopic probe to determine the temperature dependence of penetration depth and the superfluid density, investigate the physics of the vortex state, and search for time reversal symmetry breaking (TRSB). This investigation of two members of the Th7Fe3 family of materials is particularly interesting and timely, as we have recently found TRSB in the related NCS superconductor La7Ir3. By comparing the NCS (La7Pd3) and CS (La7Ru3) cases, we will be able to investigate further the role inversion symmetry plays in controlling the physics of these systems.