In his Homilies on First Corinthians, John Chrysostom (347-407 AD) writes the following regarding 1 Corinthians 8:6:
John Chrysostom - Homily 20 on First Corinthians
6 Nor yet, if you observe, has he distributed the names as if belonging exclusively, assigning to the Son the name Lord, and to the Father, God. For the Scripture uses also often to interchange them; as when it says, "The Lord says unto My Lord" (Psalm 110:1); and again, "Wherefore God Your God has appointed You" (Psalm 45:7); and, "Of Whom is Christ according to the flesh, Who is God over all" (Romans 9:5). And in many instances you may see these names changing their places. Besides, if they were allotted to each nature severally, and if the Son were not God, and God as the Father, yet continuing a Son: after saying, "but to us there is but One God", it would have been superfluous, his adding the word "Father", with a view to declare the Unbegotten. For the word of God was sufficient to explain this, if it were such as to denote Him only.
And this is not all, but there is another remark to make: that if you say, "Because it is said 'One God,' therefore the word God does not apply to the Son"; observe that the same holds of the Son also. For the Son also is called "One Lord", yet we do not maintain that therefore the term Lord applies to Him alone. So then, the same force which the expression "One" has, applied to the Son, it has also, applied to the Father. And as the Father is not thrust out from being the Lord, in the same sense as the Son is the Lord, because He, the Son, is spoken of as one Lord; so neither does it cast out the Son from being God, in the same sense as the Father is God, because the Father is styled One God.
Above, John Chrysostom says that "God" and "Lord" are not to be understood as applying to the Father and Son respectively, in an exclusive way. To argue for this point, he cites three passages in which he apparently believes that "God" is assigned to Jesus, or "Lord" is assigned to God:
In short, John Chrysostom is attempting to argue that the terms "God" and "Lord" are ambiguous, which strictly speaking, is true, but it is not true in every context. In 1 Corinthians 8:6, the Apostle Paul uses them unambiguously to establish the two positions of authority for Christians in the New Testament. There is not a single instance in which the Father is called "Lord", in distinction to the "God" Jesus, in a passage like this which speaks of the two positions. Bringing up the fact that the terms can be applied to the other subject in other contexts is just confusing the discussion, and reading ambiguity into a place where there is no ambiguity.
John Chrysostom then appears to argue that mentioning "the Father" would be in some sense superfluous if He had intended to say that the Son was distinct from God, but his point is not exactly clear. "God the Father"/"God our Father" is an established epithet in the Bible, and "the Father" is a primary name by which God is called all throughout Paul's epistles. Although, sometimes the Apostle Paul does in fact just use "God" without that epithet, and it is clear that he means to refer to the Father (1 Corinthians 1:4, 1:9, 1:24, 1:30, 3:23, etc.). So, him using that identifier here is not superfluous - it is in line with how he writes, and what he calls God throughout his writings.
Then, John Chrysostom appears to argue that if the Father being called the "one God" excludes Jesus from being God, then Jesus being called the "one Lord" would exclude the Father from being Lord. But, this is the same misunderstanding of the position of "Lord" established in the New Testament that was addressed earlier. Jesus is not the "Lord" in the ultimate, underived sense that the Father is the Lord God Almighty. He is the Lord Messiah, who has been exalted to Lordship by His Father, who is God. The verse in question, 1 Corinthians 8:6, is one of the passages which demonstrates the distinction between the "one God" and the "one Lord" under God, and from the context of this epistle, it is very clear that the "one Lord" is under the "one God" (1 Corinthians 3:23, 11:3, 15:27-28).
In summary, the term "God" in 1 Corinthians 8:6 is not ambiguous. No others besides the Father (Yahweh) are ever called the "one God" in a context like this. Neither is the position of "one Lord" which the passage speaks of ambiguous, as it does not refer to Yahweh, but to the Lord Messiah, who is explicitly distinguished from Yahweh (Psalm 110:1 - Yahweh tells this Lord to sit as His right hand).