The One God is the Father. The One Lord is Jesus Christ. This language is being used to differentiate between the two. Paul was a monotheist, moreover the expectation of explicit trinitarian terminology would be an anachronism in the New Testament.
This is however a controversial passage even among scholars.
James Dunn writes in "Did the First Christians Worship Jesus?" pg 108-109 about Bauckham's book "God Crucified"
Bauckham insists: "the only possible way to understand Paul as
maintaining monotheism is to understand him to be including Jesus in the
Shema ... is is identifying Jesus as the 'Lord" whom the Shema affirms
to be one... the unique identity of the one God consists of the one
God, the Father, and the one Lord, his Messiah."
However, the point is not quite as clear cut as Bauckham suggests. For the question arises as to whether Paul did indeed intend to 'split the Shema'. It is quite possible to argue, alternatively, that Paul took up the Shema, already quoted in 8.4 ('there is no God but one'), only in the first clause of 8.6 (reworded as 'for us there is one God, the Father') and to that added the further confession, 'and one Lord Jesus Christ'. Bauckham argues to that 'the addition of a unique Lord to the unique God of the Shema would flatly contradict the uniqueness of the latter'. But if anything the fuller confession of 8.6 could be said to be a more natural outworking of the primary conviction that 'the Lord (God) has said to the Lord (Christ), "Sit at my right hand..."'(Ps. 110.1), a confession set precisely in contrast to the gods many and lords many of the Graeco-Roman worship.
Dunn continues to note that the use of prepositions in the later clauses indicate God (the Father) as the source/ origin of everything and the goal to which Christians are to be directed while the one Lord (Christ) is the mediating agent "through whom all things and believers have effective being."
Further he notes that this agency is equivalent to the way in which Wisdom and the Word were being used, as describing divine agency.
I would argue that the legitimacy of Paul's ministry largely hinges on if he properly understood the Shema. And if he is indeed splitting it (separating the identity of the one God from the one Lord (YWHW) the legitimacy of his ministry is compromised. If however we take the view that the one Lord is further confession we may well regard it in the sense that Luis XIV declared 'One King, One Law, One Faith." they are consecutive unique entities. In this sense the "One Lord" is unique not in that he shares the godhead, but that he is the prophesied messiah whose reign will not end, the ultimate divinely appointed king. Paul's claim that Jesus is the Messiah the Christ, is not exclusively religious, it is by its very nature a political statement about Israel's national destiny which he sees (prophetically) fulfilled in Jesus of Nazareth.