We have undertaken a comparative study on the effect of Li-doping on the magnetic property of Cu(OH)2-CuO composite. A simple chemical solution route is used to synthesize the doped and undoped composite samples, while the structural characterization was investigated using X-ray Diffraction studies. With 1% Li-doping in Cu(OH)2-CuO, we discover dramatic changes in the magnetic features of both CuO and Cu(OH)2, which is directly reflected in the temperature-dependent magnetic susceptibility and field-dependent magnetization curves. It is found that the antiferromagnetic transition temperature for monoclinic CuO is reduced from 230 to 216 K while the same in contrast is enhanced from 55 to ~85 K for orthorhombic Cu(OH)2 upon Li-doping in Cu(OH)2-CuO. More importantly, the shape of the magnetic susceptibility curve, as observed in Li doped Cu(OH)2-CuO, indicates the weakening of the quasi-1D property of CuO. The present study demonstrates that the underlying magnetism (dimensionality as well as collective magnetic ordering) for both CuO and Cu(OH)2 in Cu(OH)2-CuO can be tailored by Li-substitution.