2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/216930A C*-metric algebra consists of a unital C*-algebra and a Leibniz Lip-norm on the C*-algebra. We show that if the Lip-norms concerned are lower semicontinuous, then any unital *-homomorphism from a C*-metric algebra to another one is necessarily Lipschitz. It results that the free product of two Lipschitz unital *-homomorphisms between C*-metric algebras coming from *-filtrations is still a Lipschitz unital *-homomorphism.10 pages. *-homomorphism between C*-metric algebras added to Definition 2.5. An error in Proposition 3.2 is corrected. A few minor improvements elsewhereOperator Algebras46L87; 46L05text