THE OLDEST GREEK TEXT OF MICAH 5:4 LXX "...THE NAME OF ( JEHOVAH ) HIS GOD..." HAS THE TETRAGRAMMATON IN ANCIENT HEBREW IN THE GREEK TEXT

Above is an image of the Greek MSS or manuscript (8HevXIIgr) also known as (Göttingen 943). 

NOTE THE THIRD AND FOURTH LINES IN PRINTED GREEK FROM THE BOTTOM

The Greek text is written with Hebrew/Aramaic forms of the divine name or Tetragrammaton right in the middle of the Greek text.

It does not substitute the Tetragrammaton with “Lord” or “God” as newer copies of the Septuagint do.

Hebrew    Transliteration    Strong's    English
וְעָמַ֗ד    ve·'a·mad    5975    will arise
וְרָעָה֙    ve·ra·'ah    7462    and shepherd
בְּעֹ֣ז    be·'oz    5797    the strength
יְהוָ֔ה    Yah·weh    3069    JEHOVAH
בִּגְאֹ֕ון    big·'o·vn    1347    the majesty
שֵׁ֖ם    shem    8034    of the name

יְהוָ֣ה    Yah·weh    3069    JEHOVAH

אֱלֹהָ֑יו    e·lo·hav;    430    his God
וְיָשָׁ֕בוּ    ve·ya·sha·vu    3427    will remain
כִּֽי־    ki-    3588    Because
עַתָּ֥ה    at·tah    6258    time
יִגְדַּ֖ל    yig·dal    1431    will be great
עַד־    ad-    5704    against
אַפְסֵי־    af·sei-    657    to the ends
אָֽרֶץ׃    a·retz.    776    of the earth

Young's Literal Translation of the Hebrew: "...And he hath stood and delighted in the strength of JEHOVAH, In the excellency of the name of JEHOVAH his God, And they have remained, For now he is great unto the ends of earth..."

Now compare this with the Modern Greek text and translations of the Septuagint:

Micah 5:4 ( MODERN ) Greek OT: Septuagint with Diacritics
καὶ στήσεται καὶ ὄψεται καὶ ποιμανεῖ τὸ ποίμνιον αὐτοῦ ἐν ἰσχύι κυρίου καὶ ἐν τῇ δόξῃ τοῦ ὀνόματος κυρίου τοῦ θεοῦ αὐτῶν ὑπάρξουσιν διότι νῦν μεγαλυνθήσεται ἕως ἄκρων τῆς γῆς

Charles Thomson's English Translation of the Greek Septuagint (LXX) Bible: "...thren shall turn to the children of Israel. And they will stand i and look and the Lord will feed his flock with majesty; and in the glory of the name of the Lord their God they shall subsist; because they shall now be magnified to the ends of the earth..."

Brenton's English Septuagint (1851): "...And the Lord shall stand, and see, and feed his flock with power, and they shall dwell in the glory of the name of the Lord their God: for now shall they be magnified to the ends of the earth..."

THE HOLY ORTHODOX BIBLE THE GREEK SEPTUAGINT IN ENGLISH: "...And He will stand, and see, and shepherd his flock in the strength of the Lord, and they shall dwell in the glory of the name of the Lord their God; for now they will be magnified to the ends of the earth..."

This is a Messianic text talking about Jesus - and who?

"...( HIS ) GOD..."

And who would that God of his be?

John 20:17 

"...MY FATHER and your Father and to ( MY ) GOD and your God..."

Matt 6:9 

"...( OUR ) FATHER in heaven let YOUR ( NAME ) BE SANCTIFIED..."

Eph 1:17 (The Translators New Testament): 

"...The glorious FATHER WHO IS THE GOD ( OF ) our Lord Jesus Christ..."

JEHOVAH

The references above show Jesus had a GOD:

1.) BEFORE he came to the earth as a man

2.) DURING his time on earth as a man

3.) AFTER he came to earth as a man