LISP (Locator/ID Separation Protocol) has been proposed as a future Internet architecture in order to solve the scalability issues the current architecture is facing. LISP tunnels packets between border routers, which are the locators of the non-globally routable identifiers associated to end-hosts. In this context, the encapsulating routers, which are called Ingress Tunnel Routers (ITR) and learn dynamically identifier-to-locators mappings needed for the encapsulation, can cause severe and long lasting traffic disruption upon failure. In this paper, thanks to real traffic traces, we first explore the impact of ITR failures on ongoing traffic. Our measurements confirm that the failure of an ITR can have severe impact on traffic. We then propose and evaluate an ITR synchronization mechanism to locally protect ITRs, achieving disruptionless traffic redirection. We finally explore how to minimize the number of ITRs to synchronize in large networks.