During the last years several papers studying conditional functional equations have appeared. They mostly deal with equations satisfied on some restricted domain and many among them concern equations postulated for orthogonal vectors. In this paper, we define the conditional homomorphisms with the predecessor defined by $\gamma(x)=\gamma(y) with an even mapping $\gamma$. Then, using a fixed point theorem, we investigate the stability of the conditional homomorphisms in Lie $C^*$-algebras.