In Low-power and Lossy Networks (LLNs), multicast communications accommodate many interesting applications ranging from firmware installation and upgrades to resource discovery and utilization. However, performing multicast in LLNs has shown to be less efficient and lacks reliability when compared with unicast. This is especially the case under radio duty cycling mechanisms employed by LLNs in order to save energy and hence extend the network lifetime. In this paper, we present a technique to enhance the performance of multicast burst forwarding in duty-cycled LLNs. The proposed mechanism has been implemented in Contiki OS and evaluated in both testbed experiments and cycle-accurate simulations. Results show a considerable increase of multicast burst throughput (more than 8 times) accompanied with an important decrease in energy consumption (about three times) and transmission latency (at least 35%). Finally, the proposed mechanism was integrated with a multicast-based service discovery protocol and demonstrated noticeable improvements.