This paper deals with the problem of broadcasting messages and lifetime in wireless ad-hoc and sensor networks. The study is based on the best known localized algorithm, namely LBIP, which is based on a centralized one, BIP, whose principle consists in constructing a broadcast tree rooted on the source node, taking into account the specificities of wireless networks. Even if LBIP has excellent performances regarding energy consumption, it selects for each broadcast the same nodes to retransmit the message; if the source of the broadcast, the base station in a sensor network, is always the same, this will lead to deplete quickly the energy of relay nodes. In this paper, we propose DLBIP, a new localized broadcast algorithm based on LBIP, which dynamically changes the broadcast tree to balance energy consumption on nodes without any additional messages. We show that proposed strategy can significantly increase the number of broadcasts before the network failure. We provide simulations results that clearly demonstrates the lifetime enhancement due to our optimization.