The transliteration of the Greek is "Lagcano" and means to obtain by lot or by divine allotment. The word appears elsewhere in the NT in 2 Peter 1:1
"Simon Peter, a servant and an apostle of Jesus Christ, to them that have obtained like precious faith with us through the righteousness of God and our Saviour Jesus Christ:
and John 19:24
They said therefore among themselves, Let us not rend it, but cast lots for it, whose it shall be: that the scripture might be fulfilled, which saith, They parted my raiment among them, and for my vesture they did cast lots. These things therefore the soldiers did.
There is no mention anywhere that I've found of the word ever indicating any kind of voting or balloting.
According to the custom of the priest's office, his lot was to burn incense when he went into the temple of the Lord.