I've considered the use of "in-situ," which may be the best match. In-situ seems to have a shade of meaning connoting an original location, where I am looking for something more along the lines of "Where it was meant to be."
Technically, in its intended environment or in its intended setting:
... [T]he ultimate objective of the Engineering and Manufacturing Development phase [is] [t]o demonstrate an affordable, supportable, interoperable, and producible system in its intended environment.
– answers.com, as in countless other browser matches for ‘intended-environment’. (Browser matches for ‘intended-setting’ are flooded by references to control panels and, appropriately, jewelry.)
Colloquially (and more concisely), in its element:
Be in a situation or environment that one particularly likes and in which one can perform well:
She was in her element with doctors and hospitals. – oxforddictionaries.com
A fish out of water is out of its element. – EL&U: What does “You're out of your element” mean?
Latin surely has a perfect and obscure two-word phrase for where intended while, as noted in the question, in situ does not apply because it is taken to mean in the original environment.
Please note a subtle distinction between an original and a natural environment. Glibly put, original refers to origin whereas natural refers more to essential nature. An artificial creation may originate in a factory or laboratory but everything about its purpose, including its intended setting, is natural for it.