The Yuna Connection
This section addresses the early misconceptions of Lenne as a duplicate of Yuna, making her appear to be bland carbon copy. I will also state how Lenne serves a functional role in the story and for Yuna's character development.
First Impressions
When promotional images for FFX-2 first came out, nothing was known about Lenne and she was dubbed a Yuna-doppelganger based on their matching dress sphere costumes and, alledgedly, similar facial features. Even after the game had been played, some people still think of her as an Expy - a character ripped off from another popular character when creating sequels and spin-offs.
Even in the beginnings of the game, it's quite obvious that they have some sort of bond. Lenne and Yuna share a body in a way. Lenne's spirit, after death, attached itself to the Songstress sphere, which now is equipped to and belongs to Yuna. The connection between these two is so strong that Lenne's emotions can even influence Yuna's. Lenne's memories can also assault Yuna's dreams, causing Yuna to place herself in Lenne's position, and Tidus in Shuyin's position, within the dreams.
It is notable that Lenne connected herself so well to Yuna, despite the dress sphere having been used by others in the past. This is possibly due to either Yuna's strong spiritual power, Yuna's extended use of this sphere, or Yuna's relation to Tidus, who is indirectly connected to Shuyin, which Lenne's spirit may have sensed.
Distinctions
I find the belief that Lenne is a Yuna Expy to be ridiculous, especially after playing through the game. They are different both in appearance and personality.
Physically, Lenne looks older than Yuna, despite having died at the young age of 19. Though Spira doesn't have the same ethnic markers that our world does, Lenne and Yuna look distinct enough so that they would appear to be from different cultures if transferred to the real world. Lenne has olive undertones with bold features, while Yuna has a cherubic face with warm pink undertones. This is most evident in their concept art and drawings by Nomura. The only reason some people are deluded into believing they are similar looking is because of a certain promotional image circulated online which showed Lenne and Yuna in songstress outfits side by side. When placed adjacent in matching settings, an illusion is created that the two resemble each other.
Aside from the clear dedication to their responsibilities, their personalities are fairly different as well. While both show sadness over the fate of their lover, Lenne's current state is a wistful acceptance while Yuna's is a uncertain yearning. It makes sense since Lenne has has been dead and lingering for quite some time, while Yuna has only recently gone through her coming-of-age phase (the huge, life-changing trials she faced in FFX). As Janice at Pearl mentions, their body language is very different. You can see during their duet on the Thunder Plains that Lenne has very open, elongated movements, while Yuna has short movements close to her body. This reflects their personality distinctions.
Parallels
Shuyin/Lenne are meant to parallel Tidus/Yuna, rather than be uncreative emulations.
In terms of utility, the resemblance between Tidus/Yuna and Shuyin/Lenne acted as an important plot device. It led to confusion for both the players and the cast. It also was the catalyst that pushed Yuna into leading the journey she does in FFX-2. While Yuna would probably find herself aiding in issues of political strife regardless, the confusion of identities made the events personal for Yuna. And character angst means more character development for the player to examine.
On another level, Shuyin and Lenne forces us to take a look at love and loss from a bigger perspective, so as to examine Tidus and Yuna' relationship from that standpoint as well. So often humans forget about history, or feel like our lives are too different from those of that era to see the similarities. Thus, humans don't learn from history, and are doomed to repeat its mistakes.
Chrissy of Will says that Yuna's deals with the big issue of sacrifice in the sequel. In FFX, Yuna was hesitantly accepting of sacrifice, or at least of her own and of the tradition that promoted it, and saw the world in terms of the greater good. In FFX-2, she's changed. She holds firm the belief that sacrificing human life is never something to settle on anymore. She felt the effects of losing her friends and lover in the last game. Shuyin and Lenne represent the civilian sacrifices that both cities made over their petty disputes. Their story gave Yuna and the players a way to relate personally to the many people who had their futures stolen from them.
Oddly, Yuna resembles Shuyin more than Lenne. Both remain behind after watching their lovers die. Both are witnesses to the senselessness of war in the past, and the repetition of violent history in modern times. Yuna could go down the same road of anger and hate that Shuyin went down. Many of Spira's most destructive antagonists (Shuyin, Seymour, and Yunalesca) justify destruction because they could not see any good possibilities in the world after their loved ones' deaths. I know most people think Yuna's far too pure to be in the same category. But I look at human nature darkly; we're capable of dramatic change. Yuna could have been like this. Shuyin represents one end of the spectrum for possible paths in her life, the one of aggression and action. Meanwhile, Lenne represents the other course of action, one of faith and acceptance.
Summary
While Shuin may have been the direct inspiration for the Fayth who created Tidus, Yuna just really serves as a vessel for Lenne until past problems are solved. Lenne shares some similarities, but mostly differences, with Yuna. These traits are just enough for Yuna to empathize with Lenne's tragedy, but also to learn from Lenne so that Yuna can solidfy her own perspectives on life and death.