Locator/ID Separation Protocol (LISP) is an efficient proposal for solving the severe routing scalability problems existing in the current IPv4-based Internet and the future IPv6-based Internet. However, the basic LISP architecture does not specify how to support mobility in detail. As mobility is a fundamental issue faced by the future Internet, LISP mobility architecture (LISP-MN) was proposed recently to extend LISP to support mobility. Nevertheless, LISP-MN is a host-based mobility approach which requires software changes in end systems. To some extent, such a design breaks the primary design principles of LISP, which is a network-based protocol and requires no modification to the hosts. In addition, LISP-MN faces the same inherent problems as other host-based approaches (e.g., MIPv4, MIPv6), such as handover latency, packet loss, and signalling overhead. To solve the above problems, this paper proposes MobileID, which is a network-based localized mobility approach for LISP. In our design, a mobile node is not aware of its mobility and does not participate in handover signalling. Instead, the network takes the responsibility for managing mobility on behalf of the mobile node. We present a general overview of MobileID architecture, and introduce the detailed protocol operations in terms of the basic MobileID handover process and the route optimization procedures. Furthermore, we describe a MobileID analytic model, and compare MobileID handover performance with three representative mobility solutions, i.e., LISP-MN, MIPv6 and PMIPv6. Numerical results show the superior performance of MobileID. The handover latency of MobileID is much lower than those of LISP-MN and MIPv6, and it becomes lower than that of PMIPv6 in case of a long wireless link delay.