Question with "ne (呢) to be responded with "呢"?
我们一起吃饭呢？

This sentence is probably grammatical, but why would we ask ourselves the question? 呢 is usually used in a wh- question, such as what, when, where, etc. E. g.  你干什么呢？ 你什么时候去的呢？你在哪里找到他的呢？

我们一起吃饭呢。

This sentence is correct. It expresses we are currently eating. Somehow, this use of 呢 suggests the progressive tense. E. g. 我们看书呢 suggests 我们正在看书呢。
The rule probably makes sense in this scenario.

A: 你吃饭呢？B: 我吃饭呢。