Can I have a "remark" after a "lemma" before its "proof"? I've developed a lemma which is accompanied by its proof, naturally. But the lemma is a little bit complicated and I'd rather present some more explanations about it, before digging into the proof.

I'm an engineering student with pretty trivial experience in formal argumentation. So, I'm wondering whether I can put a remark section after the lemma to enlighten the reader about its meaning, then presenting the proof.

Actually, as I checked some proofs, authors often consider extra explanations after the proof. But I believe that such explanations are necessary before the proof, in this case.
Sure, you can do that -- many math textbooks have cases where they state a theorem, then proceed to give some intuition about what it means, applications of it, until finally the proof appears. (In some applied fields it is even the preferred publication style to postpone proofs that don't directly illuminate the main message of the article, all the way to an appendix).

Just make sure it is clear to the reader that a proof will follow later, so he doesn't think the proof is supposed to be so obvious that you don't even deign to give it.

In other words, don't just put "Remark." at the beginning of a paragraph and then start blathering. Write something like


  Before we prove the lemma, let's observe that it doesn't actually contradict the results of the previous section ...


(or whatever).
In my opinion, yes, since etymologically it is a proposition which is taken for granted, and the proof thereof is postponed (λῆμμα = ‘what is taken’ or ‘what is given’).