Albert Barnes Commentary 1 Chronicles 24:6

"And Shemaiah the son of Nethanel the scribe, who was of the Levites, wrote them in the presence of the king, and the princes, and Zadok the priest, and Ahimelech the son of Abiathar, and the heads of the fathers` [houses] of the priests and of the Levites; one fathers` house being taken for Eleazar, and one taken for Ithamar." — 1 Chronicles 24:6 (ASV)

Wrote them before the king - That is, they wrote down their names as the lots were drawn.

Ahimelech the son of Abiathar - This is an incorrect reading. It should be “Abiathar, the son of Ahimelech.” See the note on 2 Samuel 8:17.