16 months ago, I finished a paper A and submitted it to a journal X. It is currently still under review. (For the journal's defence, it must be said that the paper is quite long - 89 pages).
This paper contains a proposition (let's call it A.1) whose proof relies on a lemma (let's call it A.2). However neither this proof, nor even the statement of Lemma A.2, have been given explicitly in paper A. Instead, I just wrote: "the proof of Proposition A.1 is analogous to the proof of Proposition a.1 from my earlier paper a".
(That earlier paper contains a detailed proof of Proposition a.1, which is done by using a lemma a.2. The results a.1 and a.2 are basically special cases of A.1 and A.2; the statements, and proofs, of the results A.x are very closely parallel to the statements and proofs of the results a.x - you can obtain the former from the latter by a simple search-and-replace.)
In the meanwhile, I wrote another paper B, that heavily relies on the results of paper A. In particular, at some point, I actually needed lemma A.2. So I made explicit the statement of A.2, and refered to paper A for the proof.
I submitted paper B to a journal Y, where it was rejected. The editor said that the result was not good enough for the journal (fine; I'll aim lower next time), but also said that the reviewers complained about the reference to paper A for the proof of A.2 (which did not explicitly appear there). They were understandably confused by this; reading my paper failed to convince them that my argument has no gaps.
Is it acceptable to email the editor of journal X and send them an updated version of paper A, where I make explicit the proof of Proposition A.1 (by stating and proving Lemma A.2)?
Now to rebut some of the obvious answers:
Redoing the proof of lemma A.2 in paper B is of course technically possible, but would require reintroducing a lot of formalism from paper A (Proposition A.1 appears on page 83 of paper A... and the whole paper B is only 26 pages long!) Besides, I feel that Lemma A.2 really belongs in paper A (it is after all an essential step to prove Proposition A.1, so it is already implicitly present there). I would really like to avoid this option at all costs.
Waiting for the answer from the journal X would mean holding up the publication of paper B, which is very costly for me: in the current climate, I feel that publishing as much as possible as early as possible is critical to secure a permanent job.