A series of fixed frequency dielectric measurements shows dielectric relaxation in La2CuMnO6, with a dynamic (Arrhenius to Arrhenius) crossover at T-C. The external magnetic field alters the relaxation parameters in the vicinity of crossover and induces an unusual trend in the magnetodielectric coupling around T-C. A large magnetodielectric coupling of 55% (at 68 K, 4 kHz) and 61% (at 105 K, 285.8 kHz) under a small magnetic field of 5 kOe is discovered. Presence of ferromagnetic short-range correlations above T-C and a sign reversal of magnetoresistance around T-C are observed. Specific heat analysis revealed the presence of ferromagnetic, variable range hopping active charge localized state. The presence of ferromagnetic short-range correlations and the influence of a core-grain dominated magnetoresistance on the Maxwell-Wagner interfacial polarization are responsible for the observed large magnetodielectric effect. Both the magnetic ordering and external magnetic field control the electric dipole relaxation in the material.