We investigate the interplay between the lattice, charge, and spin dynamics in charge-ordered high Tc cuprate La1.875Ba0.125CuO4(Tc=4K) based on the inverse Laplace transform (ILT) analysis of the La139 nuclear spin-lattice relaxation rate 1/T1 (dubbed ILTT1 analysis hereafter). A major thrust of the ILTT1 analysis is that one can deduce the probability density function P(1/T1) of distributed 1/T1. We demonstrate that 1/T1lm, defined as the log mean (i.e., the center of gravity on a logarithmic scale) of P(1/T1), can be well approximated by 1/T1str deduced from the phenomenological stretched fit; however, P(1/T1) can provide much richer insight into how the lattice, charge, and spin fluctuations and their distribution develop near and below the long-range charge order at Tcharge∼54K. Upon entering the charge-ordered state, a divergent increase of 1/T1lm toward the spin ordering at TspinμSR≃35K is accompanied by an asymmetric broadening of P(1/T1). Even deep inside the charge-ordered state, 1/T1 at a gradually diminishing fraction of La139 sites continues to slow down as temperature is lowered, as expected for canonical superconducting CuO2 planes without enhanced spin fluctuations. The fraction of such canonical La139 sites almost disappears by ≃40K. In contrast, nearly half of the La139 sites in La1.885Sr0.115CuO4(Tcharge≃80K) still exhibit the canonical behavior without enhanced spin fluctuations even near its Tc=31K. These contrasting behaviors explain why superconductivity in La1.875Ba0.125CuO4 is more strongly suppressed than in La1.885Sr0.115CuO4 despite the lower onset temperature of the charge order.