If you are interested in the topic, this article gives a nice overview of the history and theoretical background of the Japanese Lesson Study approach, and there is also a nice list of references to dig into. In the conclusions of the article, they claim:
However, the significant features of Japanese Lesson Study, such as the use of collaborative work, working on common goals, sharing of ideas, team teaching, lesson observation and cooperation among peers seemed to exert similar impacts on all groups of participants. Participants from all glocal programs reported an improvement in their lesson planning, better pedagogical content knowledge and closer collegial relationship as a result of experiencing the Lesson Study process.
Here is the abstract of the article:
Japanese Lesson Study is a model for teacher professional learning that has recently attracted world attention particularly within the mathematics education community. It is a highly structured process of teacher collaboration, observation, reflection and practice. The world focus has been mainly due to the work of American researchers such as Stigler and Hiebert (Am Educ Winter:1–10, 1998; The teaching gap: Best ideas from the world’s teachers for improving education in the classroom. Free Press, New York 1999), Lewis and Tsuchida (Am Educ Winter:14–17; 50–52, 1998) and Fernandez [J Teach Educ 53(5):395–405, 2002]. These researchers have documented Lesson Study from the perspective of their social, cultural and educational contexts. In order to develop a deeper understanding of Lesson Study in a post-modern global world, there is a need to seek views beyond those presented from an American perspective. This paper will provide further additional perspectives from an Australian state view and a Malaysian state district view and a university view. The aim is to develop an understanding of how the different contexts have influenced the structure and implementation of the Japanese Lesson Study model.