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We prove the Proportionality Principle for the Lipschitz simplicial volume without any restriction on curvature, thus generalizing the main result in Löh and Sauer (J Topol 2(1):193–225, ) and the classical Proportionality Principle by Gromov. The cone procedure employed by Löh and Sauer, which is based on the uniqueness of geodesics in Hadamard manifolds, is replaced here by a local construction that exploits the local convexity of general Riemannian manifolds.