Princess Lana is a cute little puzzle jump and run game, which highly resembles the old NES game Solomons Key.
As for the story, I have actually no idea about it, thats what the guy of the youtube video said which I have posted below.
The game is Princess Lana, a game where you control a spunky Princess named Lana (or Lana-chan) as she hangs out in a pub looking for exciting things to do. She wants to help out people in need, so she undertakes various quests...and she is often helped out and informed by Mel-san, a servant in the pub. Simply put, Lana is the typical "caged bird" type of princess; she was constantly watched and didn't get much freedom. She grew tired of being watched all the time, so she ran away to do what she wanted.
In any case it's a pretty fun game and you should give it a try when you have some time especially if you like tricky puzzle games.
Preview
http://www.youtube.com/watch?v=vO-Tiyr8yc8
Offical Site
http://pbsweb.jp/
Download
http://www.vector.co.jp/soft/dl/win95/game/se444586.html