Double perovskite oxides A₂BBO₆ have attracted significant attention because of its eccentric multiferroic properties. Among such materials, double perovskites containing rare earth metals are widely studied due to their interesting physical, optical and chemical properties. Presently, the lead-free double perovskite La₂FeMnO₆ was synthesized using citrate combustion method. The orthorhombic phase formation of La₂FeMnO₆ with Pbnm space group was confirmed using powder X-ray diffraction (XRD) technique. The grain size was calculated to be 47.5 nm computed using Debye-Scherrer formula. The characteristics of double perovskites was investigated using Fourier Transform Infrared Spectroscopy (FT-IR) technique. The band gap energy properties were studied using Ultra-violet Visible Diffusive Reflectance Spectroscopy (UV-DRS). The calculated band gap of La₂FeMnO₆ was about 1.53 eV. The calculated experimental band gap value of La₂FeMnO₆ suggests that it could be a better candidate for light harvesting applications and other energy storage devices. The dielectric properties of La₂FeMnO was studied using Dielectric Analyser in the range of 100 Hz – 1 MHz at room temperature. From the observed results, impedance, dielectric and modulus studies support the existence of a non-Debye type relaxation peak. The material’s polarization mechanism was explained using Koop's theory and the Maxwell-Wagner interfacial polarization model highlighting the presence of relaxation behaviour in La₂FeMnO₆. These findings render that La₂FeMnO₆ a fascinating material for scientific research as well as for practical uses.