Two new lanthanide-based 3D metal-organic frameworks (MOFs), {[Ln(L)(Ox)(H2O)]n·xH2O} [Ln = Gd3+ and x = 3 (1) and Dy3+ and x = 1.5 (2); H2L = mucic acid; OxH2 = oxalic acid] showing interesting magnetic properties and channel-mediated proton conduction behavior, are presented here. Single-crystal X-ray structure analysis shows that, in complex 1, the overall structure originates from the mucate-bridged gadolinium-based rectangular metallocycles. The packing view reveals the presence the two types of hydrophilic 1D channels filled with lattice water molecules, which are strongly hydrogen-bonded with coordinated water along the a and b axes, whereas for complex 2, the 3D framework originates from a carboxylate-bridged dysprosium-based criss-cross-type secondary building block. Magnetic studies reveal that 1 exhibits a significant magnetic entropy change (-ΔSM) of 30.6 J kg-1 K-1 for ΔH= 7 T at 3 K. Our electronic structure calculations under the framework of density functional theory reveal that exchange interactions between Gd3+ ions are weak and of the antiferromagnetic type. Complex 2 shows field-induced single-molecule-magnetic behavior. Impedance analysis shows that the proton conductivity of both complexes reaches up to the maximum value of 4.7 × 10-4 S cm-1 for 1 and 9.06 × 10-5 S cm-1 for 2 at high temperature (>75 °C) and relative humidity (RH; 95%). The Monte Carlo simulations confirm the exact location of the adsorbed water molecules in the framework after humidification (RH = 95%) for 1. Further, the results from computational simulation also reveal that the presence of a more dense arrangement of adsorbed water molecules through hydrogen bonding in a particular type of channel (along the a axis) contributes more to the proton migration compared to the other channel (along the b axis) in the framework.