Luke's Gospel is written in Greek, where no similar distinction can be made.
η μητηρ του κυριου(Luke 1:43)
Searching for κυριος in the Septuagint yields:
και εφυτευσεν κυριος ο θεος παραδεισον (Genesis 2:8), and in that vein a couple of hundred references in Genesis alone.
And how do you imagine Elizabeth had her niece's baby for a "leader"?
None of the gospels were ORIGINALLY written in Greek. Yeshua didn’t address his own in any but their own native language.
Anyway, the convention was upheld by the english translators, regardless of what language they translated from. Had the reference been to “God,” it would have been rendered LORD. Elizabeth clearly refered to her Messiah,which would not have been taken as equivalent to God by a Hebrew.
These are not difficult concepts to those familiar with the word.