Unusual behavior of reentrant spin-glass(RSG) compound Lu₂MnNiO₆ Has been investigated by magnetometry and neutron diffraction. The system possesses a ferromagnetic (FM) ordering below 40 K and undergoes a RSG transition at 20 K. Additionally, Lu₂MnNiO₆ retains memory effect above the glassy transition till spins sustain ordering. A novel critical behavior with unusual critical exponents (β=∼0.241 and γ∼1. 142) is observed that indicates a canting in the spin structure below the ferromagnetic transition (TC). A comprehensive analysis of temperature-dependent neutron diffraction data and first-principles calculations divulge that a structural distortion induced by an octahedral tilting results in a canted spin structure below T_C.