Measurements of proton nuclear magnetic resonance (¹H NMR) spectra and relaxation and of muon spin relaxation (μ⁺SR) have been performed as a function of temperature and external magnetic field on two isostructural lanthanide complexes, Er(trensal) and Dy(trensal) [where H₃trensal=2,2′,2″ - tris - (salicylideneimino)triethylamine], featuring crystallographically imposed trigonal symmetry. Both the nuclear 1/T₁ and muon λ longitudinal relaxation rates (LRRs) exhibit a peak for temperatures T < 30 K, associated to the slowing down of the spin dynamics, and the width of the NMR absorption spectra starts to increase significantly at T ~ 50 K, a temperature sizably higher than the one of the LRR peaks. The LRR peaks have a field and temperature dependence different from those previously reported for all molecular nanomagnets. They do not follow the Bloembergen-Purcell-Pound scaling of the amplitude and position in temperature and field and thus cannot be explained in terms of a single dominating correlation time τ_c determined by the spin slowing down at low temperature. Further, for T < 50 K the spectral width does not follow the temperature behavior of the magnetic susceptibility χ. We suggest, using simple qualitative considerations, that the observed behavior is due to a combination of two different relaxation processes characterized by the correlation times τ_LT and τ_HT, dominating for T < 30 K and T > 50 K, respectively. Finally, the observed flattening of LRR for T < 5 K is suggested to have a quantum origin.