This article is from the Final-Fantasy and other Square Soft Games FAQ, by nickzman@eskimo.com (Nick Zitzmann) with numerous contributions by others.
You must go through the game, and finish the Black Omen before fighting
Lavos. It's the only way!
In the PSX version of the game, you must also save the system data
acquired at the end of the game before the New Game + command will
appear.
 
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