It's been reported all over that any, ANY version of Lumines works. This includes the platinum edition. The Lumines 2 doesn't work and some newer Lumines 1 games in Japan don't work either because they require 3.51. It might be that some of these platinum editions are newer copies with the 3.51 requirement built in.
http://www.noobz.eu/joomla/news/3.50-downgrader-faqs.html
http://www.noobz.eu/joomla/news/3.50-downgrader-faqs.html