This name is given to some deity in the KJV 264 different times. Is it referring to the father of Jesus, Jesus or the Holy Spirit?
Despite the fact that the question was clearly intended as an opportunity for the questioner to give their own answer, it's a reasonable question and deserves an answer. Fortunately it's not a difficult one.
"The Lord" is almost always used in the Old Testament as a replacement for the name of God, usually rendered YHWH, which the Jews considered too sacred to pronounce. "Thy God" (your God in modern language) means exactly what it says. Saying (in effect) "I am YHWH your God" is emphasizing both God's identity and his relation to Israel (who are almost always the people being addressed in this). It's approximately like saying "Elizabeth II, Queen of the United Kingdom". Either alone serves to identify her, but saying both adds emphasis and dignity.
So "The Lord thy God" just means "God", emphasizing both the person and the position he holds.
The surprising answer is below, but first let's explaine that God's Word never contradicts itself when rightly divided! Malachi 3:6 says I am the Lord I change not. Likewise, Hebrews 3:8 says Jesus Christ the same yesterday, today and forever. Again, when correctly deciphered the Bible KJV, will interpret itself. So to get the answer I read every time the phrase The Lord Thy God was used. Low and behold, it wasn't until Isaiah 43:3 that I found the answer...."I am the Lord thy God,the Holy one of Israel thy savior." Then again in Isaiah 48:17 "Thus saith the Lord, thy Redeemer, the Holy one of Israel; I am the LORD THY GOD that teacheth thee.......and leadeth thee in the way that thou shouldn't go."