Final Destination History/Lore
Many stages in the SSB universe are based on the games from which the SSB characters are drawn. But certain stages, including Final Destination and Battlefield appear to have been created specifically for SSB.
For example, the Battlefield Trophy explains (emphasis mine):
Super Smash Bros. Melee borrows settings from many different games to create its stages, but the Battlefield is an original creation. While its initial impression may strike some players as a bit ominous, the layout itself is fairly standard, lending it to serious, straightforward matches. Additionally, it's used to pit players against the Fighting Wire Frames.
However, no such confirmation exists for the similarly styled Battlefield stage.
Is there any history/lore to the Final Destination stage?
Does it come from a game, or more likely, is it also an original creation made for SSB? The Final Destination trophy, unlike the Battlefield trophy, is not particularly informative:
As time passes on this stage, the level appears to travel through a wormhole from the imaginary Super Smash Bros. Melee world into reality. You move through a cloud-filled sky over a vast mountain range, then into a deep-space vista of dark blues and purples. The scenery is as real as you get in this fantastical world.
Is there any lore or history for Final Destination?
Final Destination has no lore behind it besides that it's referred to as Master Hand's Residence. It's his home.
In different iterations of SSB, the background changes between different stages, changes color depending on Master Hands health and even changes speed at which it flies through space and time.
People have conjectured that the stage is linked with Master Hand, although no in-game proof has been provided for such theories. Another theory is that FD is the link between the subspace emissary levels, in which FD is the final stage.
For now, just enjoy the greatest stage in the game and the trippy backgrounds
For the record, a great resource and a highly verified website by the community with all kinds of information about SSB is Smashpedia. I used to use this site ALL the time in college when I played in tournaments.