In this paper, we study lag synchronization between two dynamical networks with non-derivative and derivative couplings via pinning control. We design two types of pinning control schemes, including linear and adaptive feedback controllers. With the corresponding control algorithms, we obtain two theorems on the lag synchronization based on Schur complement and Barbalat's lemma. In addition, we obtain the domain for the linear feedback gains. Finally, we provide two numerical examples to show the...