A content distribution network (CDN) where the information provider can distribute copies of contents to a group of cache servers is a very useful solution in various on-line services. An application-layer multicasting (ALM) system is a candidate technology for constructing the CDN, and can be achieved by utilizing a Locator/Identifier Separation Protocol (LISP) which is actively discussed in IETF. A mapping system which manages relationship between each multicast group and the group members (i.e., cache servers) is a core component of the system, but the centralized system requires costly resources for handling a large-scale CDN. In this study, we propose a new mapping system for the LISP-based application-layer multicasting system using distributed cloud computing technologies. The proposed system utilizes a distributed hash table (DHT)-based network consisting of a large number of LISP routers to manage the membership information of multicast groups, and shortens the start-up time needed for newly-arrived multicast members to start communicating with other members. This paper considers the performance of the proposed system by using a realistic and a large-scale computer simulation and clarifies that the mapping system can halve the start-up time compared with the simple DHT-based system.