Lenne is not a common name, and definitely not of Eastern origin: Square-Enix used katakana to write out Lenne's name for a reason, I would think.
The Scandinavian definition
According to Names and Meanings, Lenne is a pet form of Lennart—the Scandinavian form of German name Leonhard. Does this ring a bell in regard to FFVIII's infamous lone wolf? Time to give Nomura a call.
Real world association
There are several rivers named Lenne in Germany, the most famous one being Lenne of Sauerland—a heavily forested region full of nature arts. Now take a look at the composition of Spira: surrounded by large body of clear waters, where rivers acted as key travel routes. On the other hand, Sweetbox, who performed Lenne's theme song in English, is a band with German roots. Combine all those facts and take a wild guess at what they imply.
I am... is a Lenne Anthology project. ©2008-2017.