Lucifer's fall is a puzzling story, as Angels are not said to possess free will (being a gift God uniquely gave to mankind).
To my knowledge (and feel free to bring up an example if it exists), nowhere in canonical Scripture does it state this.
Jude 1:6 says, "And angels who did not keep their own domain, but abandoned their proper abode, He has kept in eternal bonds under darkness for the judgment of the great day." Or as the KJV puts it, "And the angels which kept not their first estate, but left their own habitation, he hath reserved in everlasting chains under darkness unto the judgment of the great day."
They left their home. Willingly. Leaving what was made for them, where they belong, to dwell unnaturally elsewhere.
There is a strange quality, however, where angels in heaven gladly and willingly and obediently do God's will and worship Him without exception; I imagine there's no doubt or disobedience in them. How could Lucifer have become so prideful and then taken down a third of the angels with him? It's hard to say. But the fallen angels have no means of salvation, and the angels in heaven have no need for saving grace.
One thing Scripture would seem to imply is that the angels would love to spread the gospel to man (that Christ died for the sins of all and was raised up), but are not allowed to, being a work of the Holy Spirit in man. I Peter 1:12 says, "It was revealed to them [the prophets] that they were not serving themselves, but you, in these things which now have been announced to you through those who preached the gospel to you by the Holy Spirit sent from heaven—things into which angels long to look."
I've heard it said that this could mean they're looking down and wondering why Christians aren't being more busy in spreading the good news. The angels desire to do so,
long to, and yet are unable. That's a privilege that God gave only to men and women.