Yes. In Benjamin L. D'Ooge's book Latin For Beginners (1911), it is written that "an appositive agrees in case with the noun which it explains" (p. 35). D'Ooge gives these examples:
Lesbia ancilla est bona. -> Lesbia the maidservant is good.
Fīlia Lesbiae ancillae est bona. -> The daughter of Lesbia the maidservant is good.
Servus Lesbiam ancillam amat. -> The slave loves Lesbia the maidservant.
The book is in the public domain and can be acquired here: https://www.textkit.com/learn/ID/108/author_id/13/
It's an old question but anyway, this answer is for myself and others lol
"Lingua Latina" is a compound word means "latin language" and this is a feminine word in nominative form. So far, it's ok.
So, why we use it in a different form here? like; "linguam latinam"
It's because the word is the direct object of our sentence here. How do we know it's the direct object? Because when we ask "what do I learn?" the answer is "latin language"
If I ask this question in latin; "quid disco?" the answer should be "linguam latinam" and the name for this form called "accusative" it's a word case for direct objects like this one.
so why we should use particularly "linguam latinam" but not some other random letters? because it's the nature of latin language. there are rules for conjugation of the words. so as a word like this; "1st declension feminine noun" the rule for accusative is putting an "m" at the end of it.
lingua latina > linguam latinam