Both bittersweet and melancholy, these short manga evoke the emotion of loneliness. Another similarity is the gothic lolita fashion that both protagonists wear. The protagonists of both are merely objects but their sorrow is strong and relatable. They yearn for someone to stay with them but time after time, the people they meet have to leave or pass away.
In my opinion, I Am a Piano (from Le théâtre de A) has better art with colour and makes better use of space, stirring up the same emotions as Lonesome Eden in a lesser number of pages. However, Lonesome Eden's plot is meatier as it has more pages to work with and uses the flashback and perspective flip devices to show hidden dimensions to the story. I love both equally and wholeheartedly recommend them.