Sin did cause separation from God for Lucifer.
Jesus said, "I was watching Satan fall from heaven like lightning." (Luke 10:18)
So Lucifer fell from heaven because he sinned. However, Lucifer often spurned rules and tried to go back to heaven.
We learn from the book of Job that when God had a meeting with His angels, Satan also came:
"Now there was a day when the sons of God came to present themselves before the Lord, and Satan also came among them. The Lord said to Satan, 'From where do you come?' Then Satan answered the Lord and said, 'From roaming about on the earth and walking around on it.'" (Job 1:6-8)
When God asked the devil where did he come from, God is implying that the devil no longer belongs in heaven.
We can see from this exchange that even though there is a separation from God, Satan tried to force his way back to heaven.
In fact, Satan often goes before God to accuse us of our sins and shortcomings. He did this with Job, and he also did this with Peter to ask permission to sift Peter like wheat (Luke 22:31).
The apostle John said:
"Then I heard a loud voice in heaven, saying,
'Now the salvation, and the power, and the kingdom of our God and the authority of His Christ have come, for the accuser of our brethren has been thrown down, he who accuses them before our God day and night.'" (Revelation 12:10)
So we know that for a time, Satan was going back and forth between heaven and earth, uninvited, and bringing accusations against those who believe.
However, God is disallowing this in the future, and will bind Satan and his angels and condemn them to eternal punishment (Revelation 20:10, 1 Corinthians 6:3).
Heaven has been tainted by Satan's rebellion.
That is why God will create a new heaven and new earth (Revelation 21).
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Jesus only died for humans to redeem us from sin. The same will not be done for angels who sinned.
Angels see God's face and have known His glory and righteousness. It is impossible to restore them to salvation, because they have chosen to rebel against the loving and righteous God, even though they have seen Him.
Humans while on earth do not see God face-to-face. So to us, grace has been given so that if we repent, we will be saved.
However, the same concept applies to people who have tasted greatly of God's goodness and yet fall away:
"For in the case of those who have once been enlightened and have tasted of the heavenly gift and have been made partakers of the Holy Spirit, and have tasted the good word of God and the powers of the age to come, and then have fallen away, it is impossible to renew them again to repentance, since they again crucify to themselves the Son of God and put Him to open shame. For ground that drinks the rain which often falls on it and brings forth vegetation useful to those for whose sake it is also tilled, receives a blessing from God; but if it yields thorns and thistles, it is worthless and close to being cursed, and it ends up being burned." (Hebrews 6:4-8)
For example, for someone like an early disciple of Jesus (e.g. Judas) who had seen God's miraculous works and yet fell away, he cannot be restored to salvation.
These people are without excuse, as are angels who sin are also without excuse.
We need to remember that God is fair. In His wisdom, He has provided redemption and mercy to us. In the end, those who hate God will be condemned and separated from Him forever.
"Your hand will find all Your enemies;
Your right hand will find those who hate You.
You shall make them as a fiery oven in the time of Your anger;
The Lord shall swallow them up in His wrath,
And the fire shall devour them." (Psalm 21: 8-9)