The Lebesgue integral is noted for its powerful convergence theorems - the Monotone Con- vergence Theorem (MCT) and Dominated Convergence Theorem (DCT). In 5 and 8, these two convergence theorems were proved for the Henstock integral. Nakanishi in 9 and Lee and Yyborny in 8 consider yet another but more powerful convergence theorem, called the Con- trolled Convergence Theorem (CCT), that includes the monotone and dominated convergence theorems. Paredes and Chew in 11 studied a controlled convergence theorem for Banach space valued HL-integrals. Generalized absolute continuity (ACG) plays a very signicant role in CCT. On the other hand, it is known that if a function satises a Lipschitz condition then it is ACG. It is the objective of this study to investigate some Lipschitz condition in the Controlled Convergence Theorem.