***** NOT A TEACHER *****
Wow! What a cool (!!!) question!
1. I was able to find a scholarly book on the Web. The author even draws a diagram to explain it, but it was too difficult for
me to understand.
2. He says that such sentences are an example of clause chaining.
3. He discusses "A lie is a lie is a lie."
a. He says that the noun phrase ("a lie") functions simultaneously [at the same time] as the predicate
nominative in one clause and as the subject of the following clause.
i. I guess that he means the second "a lie" is the subjective complement of the first "a lie" and is also the subject to which
the third "a lie" refers.
b. The scholar writes: "I would say that the clausal repetition renders the expression emphatic."
4. You can read his analysis by going to Google and typing in these words:
Grammar and Conceptualization page 168 a lie is a lie
This 1999 book was written by Dr. Ronald W. Langacker.
Thanks a million for the question. I learned the term "clause chaining" today -- thanks to you and Dr. Langacker.