LST has been formally recognized as one of the large research projects in Master plan 2020
Master plan 2020 has been published in the Science Council of Japan (SCJ) web site: http://www.scj.go.jp/ja/info/kohyo/kohyo-24-t286-1.html (Japanese only)
In total 146 projects are listed as large research projects, and 31 of them are categolized as the high priority ones, which include e.g., ALMA2 (continuation of ALMA), Subaru2 (continuation of Subaru), KAGRA (gravitational wave facility), and LiteBIRD (a satellite for CMB measurements). LST was not selected as the high priority projects. Nevertheless, being listed in Master plan 2020 is a very important milestone for the promotion of LST project.
You can find the two page summary of LST project in Master Plan 2020:
http://www.scj.go.jp/ja/info/kohyo/pdf/kohyo-24-t286-3-2-80.pdf (Japanese only)