Hmm...it could mean the hatred is growing. Interestingly enough though, enmity tends to mean hatred between two people or things. At one point Harle says this:
Serge, mon ami!
Your humain world
iz about to end!
At zat time, zere
shall be enmity between
you and ze world.
And later on Lynx says:
Listen to me...
The end of the human
world is nigh!
When this time comes, Serge,
there shall be a deep enmity
between you and the world!
This is not speculation
or prediction...
This is history!
Radius and Garai also use the word enmity to describe the Masamune, but most interesting is what Marle says, regarding enmity and Schala:
Use the '"song of life"' to heal
her enmity and suffering...
We entreat you, Serge!
Please save Schala...
Please!
Use the song of life
to heal her enmity
and suffering...
You're the only one
that can do it!
Anyhow, I didn't mean to bombard you with quotes, but basically the word enmity is used quite often in CC, and it's usually use to describe the relationship between two great things: Serge and his effect on the world, Schala's anger (at humanity, possibly), and Radius's relationship with the Masamune. However, the enmity Lynx is referring to is the same that Harle mentioned, and the same enmity that he mentioned earlier: Serge and his effect on the end of the human world.
I wish I picked up on this, I had no idea that enmity was another key factor in the game...