This article explores the possibility of using traffic optimization techniques within the context of the LISP (Locator/ Identifier Separation Protocol) framework. These techniques use Tunneling, Multiplexing and header Compression of Traffic Flows (TCMTF) in order to save bandwidth and to reduce the amount of packets per time unit. Taking into account that encapsulation is necessary in LISP, bandwidth can be drastically reduced in flows using small packets, which are typical of many real-time services. The ability of the LISP framework to manage the signaling of TCMTF options is also studied. An analytical expression of the savings, as a function of the different header sizes, is devised and used to calculate the maximum expected savings. Different services and scenarios of interest are identified, and this allows the consideration of tests with real traffic traces, showing the savings as a function of the multiplexing period, and demonstrating that the additional delays can be acceptable for real-time services.