Luke said that Mary and Joseph offered a sacrifice (καὶ τοῦ δοῦναι θυσίαν), according to what was stated in the law of the Lord (κατὰ τὸ εἰρημένον ἐν τῷ νόμῳ Κυρίου). They were offering a pair of turtledoves (ζεῦγος τρυγόνων) or 2 young pigeons (ἢ δύο νοσσοὺς περιστερῶν.). Leviticus, chapter 12:5-8, said that when the days of purification were completed, the new mother had to bring a lamb and a pigeon to the entrance of the tent of meeting for a sin offering and a burnt offering. If she could not afford a lamb, she could bring two pigeons or two turtledoves, which was the case here, since Mary was giving the offering of a poor person. The priest then made atonement on her behalf to make her clean. Thus, the unclean mother’s birth had to become clean with a burnt and sin offering, since childbirth was considered an unclean action. Her period of uncleanness was much longer than merely touching a dead unclean animal.
Luke further elaborated about the written Law of the Lord (καθὼς γέγραπται ἐν νόμῳ Κυρίου). In a paraphrase of Exodus, chapter 13:2, he said that every male born or opening the womb (ὅτι Πᾶν ἄρσεν διανοῖγον μήτραν) shall be designated or called holy to the Lord (ἅγιον τῷ Κυρίῳ κληθήσεται). It no longer is the Law of Moses, but the Law of the Lord God. Notice that Luke did not say first born, but just male. This presentation of the male child is similar to Hannah presenting Samuel in 1 Samuel, chapter 1:24-27. Hannah brought her young son Samuel to the Temple of Yahweh at Shiloh. There they saw the prophet Eli. Thus, she gave or lent Samuel to Yahweh and the prophet Eli. Luke made sure to point out that Elizabeth, Zechariah, Joseph, and Mary were all very good law-abiding Jewish parents.