Conventional Paramagnetism -a state with finite magnetic moment per ion sans long range magnetic ordering, but with lowering temperature the moment on each ion picks up a particular direction, breaking rotational symmetry, and results into long-range magnetic ordering.However, in systems with competing multiple degrees of freedom this conventional notion may easily break and results into short range correlation much above the global magnetic transition temperature. La2CuIrO6 with complex interplay of spins (s =1/2) on Cu site and pseudo-spin (j =1/2) on Ir site owing to strong spin-orbit coupling provides fertile ground to observe such correlated phenomena. By a comprehensive temperature dependent Raman study, we have shown the presence of such a correlated paramagnetic state in La2CuIrO6 much above the long-range magnetic ordering temperature (TN ). Our observation of strong interactions of phonons, associated with Cu/Ir octahedra, with underlying magnetic degrees of freedom mirrored in the observed Fano asymmetry, which remarkably persists as high as ~ 3.5TN clearly signals the existence of correlated paramagnetism hence broken rotational symmetry. Our detailed analysis also reveals anomalous changes in the self-energy parameters of the phonon modes, i.e. mode frequencies and linewidth, below TN, providing a useful gauge for monitoring the strong coupling between phonons and magnetic degrees of freedom. 12 eff J Mott-insulator, quantum-spin liquids, Weyl semimetals, axion insulators, unconventional superconductors and realization of the Kitaev model with spin-spin correlation [1-8]. In the current studies of double perovskite iridates and iridium based oxides i.e. Na4Ir3O8, Sr2IrO4, and Na2IrO3, in +4 (Ir 4+ , 5d 5 ) and +5 (Ir 5+ , 5d 4 ) oxidation state [9-16] shows Mott-insulating ground state with effective total angular momentum 12 eff J driven by strong SOC. Despite of intense research on double perovskite iridates, the factors facilitating the rich magnetic ground state are still under debate. Recently, the focus is on double perovskites with co-existence of 3d and 5d transition metals, such as La2RIrO6 (R = Zn, Mn, Ni, Fe, Co and Cu) [17-23], which have provided new frontier in unrevealing the complex quantum state of these materials owing to competing nature of multiple degrees of freedom. Due to the compact nature of 3d-orbitals, they have strong electronic correlation and highly quenched orbital angular momentum due to presence of non-degeneracy of d-orbitals originated from the Jahn-Teller effect, however, in contrast spatially extended 5dorbitals exhibit opposite behaviour i.e. strongly pronounced SOC and weak electronic correlation.Also, in case of 3d transition metal oxides, the pseudo-spin degrees of freedom are active owing to very weak SOC and as a result Jahn-Teller effect generate strong coupling between phonons and pseudo-spin degrees of freedom [24]. On the other hand, for 5d systems, strong SOC is expected to quench pseudo-spin dynamics. However, it has been suggested in recent studie...