If the question
我们一起吃饭呢？ is meant to suggest, then the response
我们一起吃饭呢。 is wrong, no matter what tone is applied on the second
呢.This suggestion can be made with several endings. In term of the strength of suggestion, from strong to weak:
我们一起吃饭吧？/！(Strong suggestion, with request)
我们一起吃饭吗？(Only asking, with very weak suggestion)
Please don't torture yourself to remember all these differences. Acquire them naturally. If you have to answer with the same characters as much as possible from the question, it should be:
A:我们一起吃饭吧。/！ (Let's have meal together./)
The original answer you mentioned has a different meaning:
We're having meal together (at this moment of speaking).
Now it's the complicated part:
我们一起吃饭呢？ can be understood in different ways:
我们一起吃饭呢？（呢 sounds more like 呐/na/）
Suggesting that we can have a meal together.
- Fact checking:
This sentence is used to fact-check if we are having meal together:" We are having meal together at this moment, is that true?" But this is so weird in practical dialog, because nobody ask the face-to-face person whether they are indeed together. For a lame grammatical game, it's fine thought. If this is the case, then the answer
我们一起吃饭呢。(We are having meal together at this moment.) is a correct answer.
So a better version could be:
Q: They are having meal together at this moment, is that true?
A: (Yes.) They are having meal together at this moment.
As you can see, I have to use "at this moment" a lot in this explanation. Because in English, "be doing" can mean 1) doing at this moment, or 2) on the way of doing but not yet in progress. This also happens to German, a brother of English, and it's even more ambiguous because German merges both the meanings into simple present tense "somebody do". However, Chinese doesn't have this ambiguity in tense, because you can use different positions of
了 and other small characters such as
正(at this moment),
要(is going to) to explicitly express what you mean.