Given a cooperad and an operad, one can naturally produce a DG Lie algebra which is called the convolution DG Lie algebra. I will talk about various properties of the convolution Lie algebra. I will show how the lifting property for maps from the Cobar construction can be proved using convolution Lie algebras and the old good Goldman-Millson theorem. My talk is essentially an adaptation of constructions from the paper arXiv:0707.0889 by Sergei Merkulov and Bruno Vallette to the setting of operads.