The high demand for the DS Lite in Japan was such that the updated DS Lite was put on hold. But the technology found in that model made its way to the DSi LL, according to the designers.
In addition to the details behind the DSi LL's creation, the team also mentions how they thought of many names before they chose DSi LL for Japan and DSi XL for North America and Europe. Shigeru Miyamoto suggested the name DSi Deka, Japanese for DSi Large. Other suggested names included DSi Executive, DSi Comfort, DSi Premium, and DSi Living.