John Lightfoot on Luke 10:18

[I beheld Satan, &c.] "Lucifer falling from heaven," Isaiah 14:12, is the king of Babylon divested of his throne and dominion. So is Satan in this place. The word I beheld, I would refer to this very time: "When I sent you forth I saw Satan's fall at hand, that he should be immediately despoiled of his power and tyranny." For when the Messiah had determined to exhibit himself, and, in order thereunto, to send out so numerous a multitude of persons that should publish his appearance, it was absolutely necessary, and it could not otherwise be, but that the power of Satan should sink, and his government be shaken.

It is probable these seventy disciples were sent out upon the approach of the feast of Tabernacles, and when there now remained about half a year to the death of Christ. In which interval of time Christ shewed himself more openly, both by the preaching of these persons, and also in his own personal exhibition of himself, than before he had done. All which things determining in his death, whose death was also the death of Satan, might give him a very just occasion of saying, I beheld Satan as lightning fall from heaven, thrown out of his throne and kingdom. Compare Revelation 12:8, where 'heaven' is to be interpreted 'the church.'