Being a good Jewish woman, Elizabeth would never have dared to utter the tetragrammaton in full. She said Adonai, which translates Kyrios.
You might want to check your translation. She said Kyriou...specifically, "mother of the Lord of me"
Later in verse 47 Mary does use Theo (God)....does this make Mary not a good Jewish girl??
If you check, there are 1,327 occurances of the use of God or a derivative of in the NT.
Zacharias also used God in his prophecy in Luke 1:68 and 78.