Clearly, having two identical lemmata with different numbers is just plain silly and confusing, so option 1 is out.

Option 2 is probably the easiest and most natural choice, but it does have one disadvantage: readers looking for the proof of the lemma (rather than just a statement of it) will first have to flip back to section 3, before finding out that the actual proof is in section 7. That said, it's an issue you could easily live with, especially if your paper is not absurdly long. After all, people do this all the time in applied math journals, where long or complicated proofs are routinely delegated to appendices.

The problem with option 3 is that, when you first introduce the lemma in section 3, you basically have two choices: either number it as 7.2 (which looks jarring; theorem numbers are supposed to be consecutive) or leave it unnumbered (in which case sequential readers will be confused when you suddenly start referring to a "lemma 7.2", even though they haven't seen any such lemma yet).

That said, if you really want to go with option 3, this is how I'd implement it:

"We will now apply a lemma which will be proven later in Section 7. For convenience, we will restate this lemma here.

Restatement of Lemma 7.2. If $a > 0$ and $b < 0$, then $a - b > 0$.

Proof. See Section 7 (page 123).

By applying Lemma 7.2 to equation (3.14), we see that..."

A variant of this, which might be worth considering, if the lemma in question is indeed important and used in several place, would be to give the lemma a name, as in:

"We will now apply a lemma which will be proven later in Section 7. For convenience, we will restate this lemma here.

Restatement of Lemma 7.2 (The Sign Lemma). If $a > 0$ and $b < 0$, then $a - b > 0$.

Proof. See Section 7 (page 123).

By applying the sign lemma (Lemma 7.2) to equation (3.14), we see that..."

The advantage of naming your lemma is that it signals to the reader that this lemma will be reused later, and that they should actually stop and remember what it says. By also referring to the lemma by its number, you still ensure that any readers who somehow managed to miss the initial statement can still find it by flipping to section 7.

(Also, as a bonus, if the lemma really is important and useful, you might find other authors picking up the name when they cite your work.)