Exegesis:
houtōs moi pepoiēken kurios ‘thus has the Lord dealt with me, or, treated me.’ houtōs refers to Elizabeth’s pregnancy, and the perfect tense of pepoiēken shows that the emphasis is on the present results of the Lord’s dealing with Elizabeth. The clause means to qualify this as an act of divine mercy; it is an exclamation rather than a statement, as brought out in Phillips‘ free rendering “how good is the Lord for me”. Analogous exclamations in Gen. 21.6; 30.23.
en hēmerais hais ‘in the days in which,’ ‘in the time when,’ here used in a causal sense, “now that” (An American Translation, Phillips).
epeiden aphelein oneidos mou ‘he has looked on me, to take away my reproach,’ or, ‘has taken care, or, has deigned to take away my reproach,’ preferably the former; aphelein is a final infinitive. epeidon.
oneidos mou ‘my reproach’ with an objective genitive, cf. “the disgrace I have endured” (An American Translation). The ‘reproach’ was her barrenness, cf. Gen. 30.23.
en anthrōpois ‘among men,’ goes with oneidos.
Translation:
Thus the Lord has done to me, or, better to bring out that the reference is to the state Elizabeth is in now, ‘as-this here (is) the Lord’s doing to me’ (Javanese, similarly Batak Toba and cf. New English Bible), ‘that I am like this, the Lord has done it for me’ (Bible en français courant).
He looked on me, i.e. he cared for me, gave attention to me. In some languages closely similar expressions can have the required meaning, e.g. ‘he looked-downward-on me’ (Tae,’ especially said of the gods), ‘his eye fell upon me’ (Sranan Tongo). Elsewhere the favourable meaning must be made explicit, cf. ‘to have compassion,’ ‘to look graciously,’ ‘to be kind’ (Tagalog, Hindi, Apache).
To take away, or, ‘to remove’ (Kituba), ‘to wipe off’ (Hindi, Malay), ‘to remove throw away (i.e. to remove utterly)’ (Santali), ‘to cause-to-disappear’ (Javanese).
My reproach among men, or, ‘what disgraced me in the eyes of men,’ ‘things that were causing-to-see me shame before people’ (Kituba); or, taking ‘men’ as the agent, ‘the reason why people abased (or, laughed at) me.’ The cause of the reproach or disgrace may have to be specifically mentioned, e.g. in Shipibo-Conibo, which renders the whole phrase by, ‘that they (indefinite) might not ever again reproach me for barrenness.’ For “shame” cf. on 13.17.
Quoted with permission from Reiling, J. and Swellengrebel, J.L. A Handbook on the Gospel of Luke. (UBS Handbook Series). New York: UBS, 1971. For this and other handbooks for translators see here . Make sure to also consult the Handbook on the Gospel of Mark for parallel or similar verses.