In the context of geometrically frustrated magnets, a new family of compounds A2R3Sb3O14 (A=Mn, Mg, Zn, Co; R=rare-earth ions) has been recently discovered, in which the rare-earth R ions form a tripod kagome lattice, separated by A2+ triangular layers. Among the series of compounds A2R3Sb3O14, Mn2R3Sb3O14 stands out because it forms either a rhombohedral pyrochlore (R-3m) for R=La, Pr and Nd, or a cubic pyrochlore for R=Y. Our previous studies of magnetic properties for Mn2R3Sb3O14 exhibit the absence of the LRO, deserving in-depth studies to elucidate whether these compounds feature a spin liquid. To substantiate spin-liquid ground states in Mn2R3Sb3O14, we propose ZF- and LF-muSR experiments on the three compositions of R=Y, Lu, and La. The muSR measurements of Mn2R3Sb3O14 will elucidate the nature of ground-state spin dynamics and absence/presence of time-reversal symmetry breaking.