This paper summarizes a discussion of the role of disaster-related museums in passing down memories and lessons-learned to future generations through storytelling. The 135-minute discussion was held as a breakout session entitled “The Role of Museums in Telling Live Lessons” during the 2020 International Forum on Telling Live Lessons from Disasters in Kobe, Japan. On 25 January 2020, representatives of five museums (one still under construction) engaged in disaster storytelling activities. They discussed various issues, including how to engage local communities and improve the relationship between storytelling and sustainable museum management. The participating museums were the Pacific Tsunami Museum in Hawaii, U.S.A., the Disaster Reduction and Human Renovation Institution (DRI) in Kobe, Japan, the Museum of the Mount Bandai Eruption in Fukushima, Japan, the International Tsunami Museum in Khaolak, Thailand, and the Ban Namkhem Memorial and Museum in Thailand (under construction). Museums are important venues that develop and continue disaster storytelling. All the participating museums digitally archive images, which creates the permanent inheritance of collective memory. All the museums focus on children. On the other hand, human and economic resources are required for museums to carry out their activities. The need for a museum network engaged in disaster storytelling is also discussed.