We first show that every unital endomorphism of real Lipschitz algebras of compl ex-valued functions on compact metric spaces with Lipschitz involutions is a composition operator. Next we establish a formula for essential spectral radius of a unital endomorphism $ T $ of these algebras under a condition which is equivalent to the quasicompactness of the endomorphism $ T $. We also conclude a necessary and sufficient condition for a unital endomorphism of these algebras to be Riesz. Moreover, we get a relation for the spectrum and the set of eigenvalues of quasicompact and Riesz endomorphism of these algebras. %Finally, we show that the class of quasicompact (Riesz, respectively) unital endomorphisms of these algebras is larger that the class of quasicompact (Riesz, respectively) unital endomorphisms of complex Lipschitz algebras as real Banach algebras.d
