La₂NiMnO₆ (LNMO) was prepared by a combustion method followed by heating at high temperature. Subsequently, the preformed LNMO was annealed in air, oxygen, or N₂ atmosphere and characterized by powder x-ray diffraction (XRD), neutron diffraction, superconducting quantum interference device magnetometry, and dielectric analysis. Structural studies by XRD and neutron diffraction revealed the coexistence of partially cation disordered monoclinic (31%) and rhombohedral (69%) phases in the sample annealed in air. However, the sample annealed in oxygen shows about 50:50% of monoclinic and rhombohedral phases. Relaxor-like behavior with relative permittivity of the order of 10⁴ was observed in the sample annealed in air, while relative permittivity decreases to about 200 in samples annealed in oxygen atmosphere. The magnetic properties indicate a well-defined ferromagnetic phase in the oxygen-annealed sample compared to a feeble ferromagnetic signature in the air-annealed one. The dielectric and ferromagnetism of LNMO samples have been related to formation and annihilation of oxygen vacancies.