Considering the LTW is called 'Private
Aquarium Lifetime Wish' would naturally lead one to believe the perfect fish must be in an
aquarium and not in a pond in order to complete the wish.
I finished this wish once, but finally kept my perfect fish in my inventory until I had enough to stock my individual aquariums with. I learned this the hard way, as at first I placed them in the aquariums when I caught them, but they tended to die because I did forget to feed them.
Note: You don't have to feed them when in your inventory or when placed in a chest on your lot.