When the target language does not have a certain word, there are two strategies a translator can use:
(1) As already mentioned, transliteration with an explanatory footnote is one strategy. That is when you carry the spelling of the original word right into the target document, like "baptism" from Greek. The word then may become a "loan word," carrying the meaning of the original into the target language as the reader learns the original meaning and transfers the meaning to the new word in his language. A loan word has become normal word in the target language, like "sushi" has become in English.
(2) You can translate the original word with a phrase. There is no word in Japanese for justification, so we translate it with gi to mitomeru, which is "recognized as righteous." So "sheep" in a society that doesn't keep sheep can be, "a white, docile animal."
Rendering "sheep" or "lamb" as "pig" or "piglet" is not translation, but paraphrase. It doesn't even meet the standards of dynamic equivalence, (a method which I oppose), in that the reader's response to "pig" would not be the same as a 1st century Jew's response to "sheep" by any means.
You use the term "primitive people," which I feel is a mistake. There is no such thing as a "primitive person," because tribal people, while not advanced technologically, are just as capable as the typical American, with the same brain capacity, gifts and abilities, and potential for Christ.
Also, there is no such thing as a primitive language. Tribal languages are just as complex and capable of conveying meaning as English. Though without special sets of modern technical vocabulary (engineering, medicine, etc.), they may even have their own sets of technical vocabulary not known by an American: words for snow in Alaska, words for jungle plants and animals, etc.
Edited in: One other thing. After Christianity comes, education always, always follows. Literacy is taught, being necessary for the believers to learn to read their Bible. With education comes further sophistication, so that the tribal Christian can easily learn what snow or a sheep are. If his Bible then has "pig" when he is educated enough to learn what a sheep is, he loses confidence in his Bible translation, which can be a very bad result.