Here is the verse from the LXX:
- “σὺ δὲ ὁ αὐτὸς εἶ, καὶ τὰ ἔτη σου οὐκ ἐκλείψουσιν.” (Psalm 101:28 LXXS-T)
- "And you, yourself, are he; And your years will not give out." (translation mine)
The LXX closely follows the Hebrew text:
- ”וְאַתָּה־הוּא וּשְׁנוֹתֶיךָ לֹא יִתָּמּוּ“ (Psalm 102:28 BHS-T)
- "You are he; and your years will not expire." (Translation mine)
So, to get at an answer to your question, from what I can see, the Septuagint doesn't have the words, "forever" in the text.
Perhaps the English version of the Septuagint you're using uses a more functional translation (changing the double negative, "not...give out" to "live forever)?
As it turns out, you're off a verse, so this is a revised answer:
In vs. 29, this is the Greek:
- “οἱ υἱοὶ τῶν δούλων σου κατασκηνώσουσιν, καὶ τὸ σπέρμα αὐτῶν εἰς τὸν αἰῶνα κατευθυνθήσεται.” (Psalm 101:29 LXXS-T)
- "the sons of your slaves will dwell; and their seed will be directed in a straight line forever." (translation mine)
The translator of the LXX, (as often happens in the Septuagint),took a more functional approach in translation, evidently. Here's the Hebrew:
- ”בְּנֵי־עֲבָדֶיךָ יִשְׁכּוֹנוּ וְזַרְעָם לְפָנֶיךָ יִכּוֹן׃“ (Psalm 102:29 BHS-T)
- "The sons of your slaves will dwell; and your seed will [continute to] be established in your presence."
So, the Hebrew lets us know that the seed will be established without a foreseen end (יִכּוֹן). The LXX renders that with "into the ages" (εἰς τὸν αἰῶνα).
The other challenge, from a translation point of view is what to do with the "into the ages" phrase. BDB has this listed as the definition of "Olam":
- 5769, 5865 עוֹלָם 439 n. m. long duration, antiquity, futurity <BDB, s.v. “עלם,” 761.>
Notice that it has two meanings:
So, the phrase, "εἰς τὸν αἰῶνα" ("Into the ages") can be roughly equivalent to "יִכּוֹן" ("will be established.")