No, the Tetragrammaton יהוה is never transliterated into the Greek Septuagint (LXX).
- Sometimes יהוה is not translated into the LXX (cp. Gen. 2:7 LXX).
- Sometimes יהוה is translated into the LXX as κύριος (cp. Gen. 4:3 LXX).
- Sometimes יהוה is translated into the LXX as ὁ θεὸς (cp. Gen. 4:1 LXX).
- Sometimes יהוה is translated into the LXX as κύριος ὁ θεὸς (cp. Gen. 2:8 LXX).
Hebrew does have vowels; but, these vowels were not created until approximately the 10th century A.D. The original scrolls would not have had vowels (nikkud).
In Wars of the Jews, Book V, Line 235, Josephus wrote,
τὴν δὲ κεφαλὴν βυσσίνη μὲν ἔσκεπεν τιάρα, κατέστεπτο δ ̓ ὑακίνθῳ, περὶ ἣν χρυσοῦς ἄλλος ἦν στέφανος ἔκτυπα φέρων τὰ ἱερὰ γράμματα· ταῦτα δ ̓ ἐστὶ φωνήεντα τέσσαρα.
which is translated as,
And a tiara of fine linen encompassed the head, and it was crowned with hyacinth, around which there was another golden crown, bearing the engraved holy letters. And these are four vowels.
This appears to be a contradiction, but in Hebrew, a few of the letters also function as vowels, even today. Two of the consonants doubling as vowels are י and ו, which can be transliterated as "i" and "o"/ "u," respectively. Coincidentally, these two letters (י and ו) also appear in the Tetragrammaton.
Another letter that used to function more often as a vowel, but rarely so today, is the letter ה.
In his analysis of the Isaiah Dead Sea Scroll, Fred Moeller wrote,
Just as the Masoretes invented pointings to indicate vowel sounds so the Q[umran] scribes have added some semi-vowels to the text. The use of yod, waw, and "he" are frequent.
So, like י and ו, the letter ה was another one of the immot kri'ah, or "mothers of reading" (consonants which also functioned as vowels). Thus, Josephus was not wrong. At that time, those letters may have been considered vowels.
As for the reason that κύριος is predominately used to translate יהוה, rather than יהוה being transliterated into the LXX, is that it was already the common practice of the Jewish scribes to never pronounce the Tetragrammaton יהוה whenever it appeared on a scroll. Instead, the scribes would pronounce the word אֲדֹנָי (adonai), which essentially means "lord," "master" in English, and thus, κύριος in Greek. Now, since the scribes already pronounced אֲדֹנָי for יהוה, they decided to write κύριος for יהוה when producing the Greek Septuagint, since κύριος is the (closest) Greek equivalent to אֲדֹנָי.