Many would argue that by killing the deer quickly,
the lion is showing compassion..

Compassion: Deep awareness of the suffering of another
coupled with the wish to relieve it.

As was stated in another's post about the eagles, the quick
ending of another creature's life is not based on
the creature's desire to kill for amusement, but for natural
selection purposes. We eat mutton...the meat of an animal.
By your reasoning, the killing of the animal for use
as food for us would be inhumane and therefore cruel.

Now.....there are really a couple definitions for Humane,
and one is even a variation on yours and more easily
shows how the lion isn't being inhumane.

Humane: Characterized by kindness, mercy, or compassion

and

Humane: Marked by an emphasis on humanistic values and concerns

The first one adds the quality of mercy to the definition. I believe
the lion is being merciful by making the kill quick, instead of
prolonging the deer's pain. Also notice the use of the word 'or',
meaning
that something doesn't have to posess all these qualities to
be considered humane.

The second definition really brings me to what I mostly wanted to
say about this. Humane....remove the 'e' and what do you get?

HUMAN

Humane is a word that was created as a quality of humans and other
sentient beings, not for animals. While using it to describe
the actions an animal does may make a good metaphor, it really
doesn't apply to the situation. A lion is a lion, no matter
what you want to say about it, it will act as it does cause
that is all it can do. There is no sense of cruelty in the
lion's mind.

Penned by my hand on the 21st of Scarlatan, in the year 354 AF.