This paper presents a distributed algorithm called L-REMiT for enhancing the lifetime of a source-based multicast tree in wireless ad hoc networks (WANET). The lifetime of a multicast tree is the duration from the formation of the tree to the time when the first node fails due to battery energy exhaustion. L-REMiT assumes that the energy consumed to forward a packet is proportional to the forwarding distance and channel characteristics, and that WANET nodes can dynamically adjust their transmission power. The task of extending the lifetime of a multicast tree is formulated as the task of extending the lifetime of bottleneck nodes in the tree. The number of multicast packets that a bottleneck node can forward, as determined by its residual battery energy and the distance of its farthest child node, is the minimum over all the nodes in the multicast tree. The lifetime of a bottleneck node is improved by reassigning its farthest children to other nodes in the tree with the goal of improving the lifetime of the multicast tree. Nodes only require information from their neighbors for refining the tree in a distributed manner. Simulation results show that L-REMiT has low overhead and performs better than the BIP/MIP and EWMA algorithms.