whatever you see or understand is fact to you. same goes for a lack of understanding. Animals aren't physically immortal, but mentally they cannot die as they dont understand their own death
There's no such thing as "mentally dying", as dying is a physical thing.
Animals can't understand that they are dead, but neither can humans. You can't understand that you are dead because by the nature of being dead you aren't alive to understand or be aware of anything.
The only way this can't be true is if there is an immortal soul that lives on after the death of the body.
As for whether animals are aware of their own mortality it would seem that they are as many animals engage in practices when dying, such as hiding in warm secluded places. This may be evidence of just some instinct for self-preservation rather than awareness of approaching death, but that seems difficult to prove one way or the other.