The vacancy effect in quantum spin liquid (QSL) has been extensively studied. A finite density of random vacancies in the Kitaev model can lead to a pileup of low-energy density of states (DOS), which is generally experimentally determined by a scaling behavior of thermodynamic or magnetization quantities. Here, we report detailed muon spin relaxation (μSR) results of H3LiIr2O6, a Kitaev QSL candidate with vacancies. The absence of magnetic order is confirmed down to 80 mK, and the dynamical spin fluctuations are found to be persistent at low temperatures. Intriguingly, the time-field scaling law of longitudinal-field μSR polarization is observed with the critical exponent of 0.46, exhibiting excellent consistency with scaling behavior of specific heat and magnetization data. This points to the finite DOS with the form of N(E) ~ Eν, wihch is expected for the Kitaev QSL in the presence of vacanncies.