Well, how about sentence 1 and 3? They do not contradict each other. I mean if we had only sentence 1 and 3, could we claim that sentence 3 is a metonymy?
or if we had a sentence like "Jack is like a lion" instead of sentence 2, would the result be a metonymy in this case?
[ I am not a teacher. ]
Venus, regarding your post # 3, you're welcome. I didn't remember to say that. I'm sorry. Better late than never.
Dear teachers, thank you for your answers to my comments trying to help Venus. With the due respect, my view is not the same as yours. My conclusion on the issue is based on what I read in books written by teachers too, especially Paul Fry and and Craig Kallendorf (the author or the book I've linked in my last answer).
As I'm very interested in this issue, as I said, I've studied it more profoundly and I'm pleased to share on the following Google Docs file part of the notes and sketches I've made on the issue on my notebook about Literary Science:
https://docs.google.com/document/d/17wJPpFNXpCc_hb9GjGyaBkE1m99nLaMWRR2N3P6iKHM/edit?usp=sharing
If occasionaly someone gets interested in my analysis and detect any mistake in it, I'll be interested in discussing it. Unnecessary to say that my aim is not to win a debate, but to learn.
I my view, both Sentences 1 and 2 make clear that when the author of the text refers to "Lion" in Sentence 3, he actually refers to "Jack". That's the point. In other words, it doesn't matter if we had before a metaphor (Sentence 1) or an irony (Sentence 2). Something that was said before in the text makes clear to the reader that there's a substitution of "Jack" for "Lion" in Sentence 3; and that makes of "Lion" a metoymical signifier.
Let's suppose that we have only Sentece 3 and absolutely no context (no text and not even the sound, image or video of a man entering a room). In this case, how would the reader get to know that the author of the text is saying not that a real lion entered the room, but actually a man called "Jack"? Without context, an isolated Sentence 3 necessarily conveys the idea that "Lion" is the arbitrary signifier linked to the concept of a certain animal: there would be neither a metaphor nor a metonymy.
The reader knows that "Jack", and not really a lion, entered the room because something that was written before (a metaphor/ an irony in previous sentences) gave him this piece of informátion. So there's a substituion in Sentence 3 that is only possible to make by the reading of the text. The difference to "The White House said that..." is that epistemic/encyclopedical knowlegde in a certain culture -- and not something that was said before in the text -- made possible the association between the signifier "White House" and the signified "government of USA".
"Lion" is a methaphorical sigifier or an "ironical signifier" (quotation marks because I didn't have time to read about irony as a trope and I don't know whether this expression is technically used) in Sentence 3 (as well as a metonymy) only because we had a metaphor / an irony in previous sentences that established to the reader's view an association between "Lion" and "Jack".
So
in Sentence 3 "Lion" works simultaneously as
a) a metaphor/irony, previously
made on Sentence 1/2 [the signifier "Lion" foregrounds the arbitrary signifier "Jack"];
b) a metonymy in the substition of "Jack" for "Lion", given that the metaphor/irony previously established a
intratextual (syntagmatic) contiguity between "Lion" and " (concept of) Jack", metaphorical signifier and arbitrary signified, respectively [the metaphorical signifier "Lion" foregrounds the signified "Jack" (as a concept)].
I have to make a correction. I said in my last comment that Sentence 3 was a synechdoche. After the more profound analysis I made, the one shown on the text linked above, I've conclued that it is a "simple metonymy" constructed by a direct association made
intratextually -- and not by what characterizes a synecdoche: a more complex association (a "condensation", to Jakobson) that requires the use of logic.