Limbo is unlike most games in that the only story provided by the company was the single sentence:

"Uncertain of his sister's fate, a boy enters Limbo"

Everything else was left open to the interpretation of the player. Many theories have been suggested as to what the various game elements might represent as well the overall story arc but it all remains in the realm of speculation. A decent article about the making of Limbo can be found here.

-----------------

In creating a game like Limbo I would give serious consideration to its minimalist approach i.e. there are no overtly complex game behaviours, puzzles are relatively benign (yes the many death scenes on failure are a treat) but no more than three levels deep in terms of solving them. It has been suggested and somewhat confirmed by Arnt Jensen that much of his inspiration is drawn from his childhood experiences and literature which perhaps might be the best suggestion for you i.e. draw upon your own experiences and create a world that meets your requirements.