[count-your-change]

Fragments of the Septuagint from the first century do have the tetragrammaton in it so it would appears likely that early copies did the same at Ps. 110.

[kosta50]

Fragments of the Septuagint from the first century do have the tetragrammaton in it so it would appears likely that early copies did the same at Ps. 110.

Yes, that is a relatively recent discovery. But it makes sense. "Losing" the tetragrammaton was one way of "Christianizing" the Old Testament. Otherwise verses such as Matthew 22:42-45 would be pointless.

For example, the Greek text does not distinguish one Lord from another.

τῷ Δαυιδ ψαλμός εἶπεν ὁ κύριος τῷ κυρίῳ μου κάθου ἐκ δεξιῶν μου ἕως ἂν θῶ τοὺς ἐχθρούς σου ὑποπόδιον τῶν ποδῶν σου [Ps 109 LXX, 110 MT]

This makes it easier to claim that one is the same as the other, that they are related or equal. In Hebrew, it is not only clear that they are not the same, but that one is divine and the other one is not.