The basic answer to your question:
Why does the Septuagint omit Isaiah 2:22 when it's in the Dead Sea Scrolls and Leningrad Codex?
is of course: because the Septuagint was not translated from the Dead Sea Scrolls or the Leningrad Codex.
That said, the more satisfying answer will be harder to come by. As in most cases where we see a discrepancy between the LXX and a Hebrew text, the basic possible explanations can be formulated in three categories:
The LXX was translated from a Hebrew text that did not include the verse. This, in turn, could be either due to:
- two parallel versions of Isaiah in use at the time, or
- a single Hebrew Isaiah text to which v. 22 was a later addition.
The LXX translator omitted the verse.
The verse was omitted during the transmission of the Greek text.
In this case, nobody to my knowledge seriously considers #3.1 As such this is considered a "real" minus in LXX Isaiah.
Much ink has been spilt on the relationship between LXX Isaiah and the available Hebrew texts. The most systematic treatment I'm aware of is Mirjam van der Vorm-Croughs's The Old Greek of Isaiah: An Analysis of Its Pluses and Minuses. She considers v. 22 in the LXX to be due to a different Hebrew Vorlage.2 In support of this, she points out that most commentators on the Hebrew text of Isaiah have considered this verse to be secondary.3 This position is generally tied up with an understanding of vv. 9b - 10, which similarly introject imperatives into the otherwise 3rd person narrative, as secondary.
On the other hand, it's possible to conceive of a Vorlage without v. 22 without assuming that it is a later addition. There has been much controversy over the idea of "parallel literary editions" of Hebrew texts in circulation in antiquity. If one accepts this model, it is hypothetically possible that there existed Hebrew texts with and without the verse, and the LXX translator happened to have at hand the latter, whereas 1QIsaa and MT are descended from the former.
Finally, some have suggested that the LXX translator removed a verse which was present in his Vorlage (regardless of its originality). Van der Kooij believes this was done for rhetorical reasons:
The plus [in the LXX] of "and now" in v. 10, which means that the Lord is going to act, right now, against every one that is high and arrogant, makes the call of v. 22, not to rely on man (understood as the powerful and the arrogant), superfluous. The wording of v. 10 (cf. v. 5) actually implies that the house of Jacob put their trust in the Lord, and no longer in those who did them wrong.4
If this all seems very confusing and convoluted, you will know that you've glimpsed the tip of an iceberg. The textual relationship between the 1QIsaa, MT Isaiah, and LXX Isaiah is a complex issue that isn't always clearly distinguishable from the redaction history of the book itself.5 As with most things, the conclusion one draws largely depend on the presuppositions with which one begins.
1. This is presumably due to the absence of manuscript evidence of the verse ever present in the Greek tradition, the tendency of LXX scribes (at least in later generations) to revise toward the Hebrew, and the more general scribal tendency to add rather than to subtract text.
2. Vorlage simply refers to the hypothetical Hebrew text from which the LXX was translated.
3. Her citation includes Duhm, Marti, Gray, Wildberger, and Ulrich; I would add that Williamson's more recent commentary agrees.
4. van der Kooij, "The Septuagint of Isaiah and the Hebrew Text of Isa 2:22 and 36:7" (Brill, 2006) 382–384, quoted by van der Vorm-Croughs, The Old Greek of Isaiah: An Analysis of Its Pluses and Minuses, 380-381. I have not been able to access van der Kooij's original essay but will update this if I am able to do so.
5. For another perspective, see Eugene Ulrich, *The Developmental Composition of the Book of Isaiah. Dead Sea Discoveries 8/3 (2001), 288-305