But some people don't cosider the PSP complete without a copy. So why hasn't it shown up on the Playstation Store yet? Licensing issues.

Tweeting about this very subject, Q Entertainment said yesterday, “We would love to bring Lumines/Lumines II to the PSN store but there are complications, music licensing, was published by Namco, etc.”

They did confirm they are looking into it however. But for now, looks like no Lumines I & II on PSPgo.