LORD God of Israel is a composite name of God. It is hard to distinguish this phrase from “LORD, God of Israel” and the meaning is about the same: Yahweh (Jehovah) is the God of Israel.
LORD God of Israel in Hebrew:
Yahweh ’Elohei Yisra’el
Strong’s Concordance numbers: 3068, 430, 3478
Bible references: Josh. 14:14 and about fifty times in total.
Hebron therefore became the inheritance of Caleb the son of Jephunneh the Kenezite unto this day, because that he wholly followed the Lord God of Israel. (Joshua 14:14 KJV)
Lord God of Israel in Greek:
Kyrios ho Theos tou Israēl
Strong’s Concordance numbers: 2962, 2316, 2474
Bible reference: Luke 1:68 (not NIV, Msg, Amp)
Blessed be the Lord God of Israel,
For He has visited us and accomplished redemption for His people (Luke 1:68)
In this verse, the name is a modified quotation from the Old Testament. In several places, God is called LORD, God of Israel (Pss. 41:13; 72:18; 106:48).