Lenne is not exactly a common name among western females. Nor eastern if we consider the fact that her name in the Japanese version was written in katakana. Since I refuse to buy the Kabalarian definition of most names I come across these days, I'm going to offer something more factual here.
Geography
Many instances of Lenne have German roots. There are two rivers named Lenne in Germany, the more famous one being Lenne of Sauerland area. The Sauerland is heavily forested and full of nature arts, which reminds me of Zanarkand's philosophy to stay away from machina. Also, as Spira is surrounded by large body of clear waters, rivers are important routes for travel. This is very much like Lenne's celebrated status in Zanarkand: her voice would connect people of different roots spiritually, which is similar to the function of rivers that physically connect people of different regions.
Crossover
According to Names and Meanings, Lenne is a pet form of Lennart, which in turn is a Scandinavian form of German Leonhard. Does this remind anyone of Final Fantasy VIII's lone wolf? While Lenne is a softer personality than Squall by the dozen, with Tetsuya Nomura as their character designer, we'd never know what connection they might have behind the scenes.