There is any number of answers to this question, some of which depend on one's personal religious beliefs.
First of all, the name Lucifer comes from Isaiah chapter 14, which refers to the king of Babylon, who laid the nations low. It talks of his pomp and splendour, how he had ruled the nations in anger, and his fate after his overthrow by the king of Persia. He had compared himself to the Morning Star (and was thus derisorily called 'Lucifer' - lucem ferre, which mean "light-bearer", a name for the dawn appearance of the planet Venus) and had thought that he would ascend into heaven and sit among the stars, but was now himself persecuted. Christian scholars misunderstood this text and assumed that it referred to Satan or the devil, a view that Judaism has never agreed with. The king of Babylon, 'Lucifer', is dead and need no longer concern us.
Satan, the real subject of the question, is actually considered in Judaism to be the loyal assistant of God, tasked with testing the righteousness of the faithful. In this view, Satan does not need saving - he is already saved.
In Christianity (and subsequently in Islam), Satan is the devil, the evil adversary of God. On this view, it would seem most unlikely that Satan can be saved. However, Christianity has its roots in Judaism and considers the Old Testament of the Jews to be its foundation. To hold that the Jews had their understanding so terribly wrong, for so many centuries, would surely require remarkable evidence, and that simply is not there. Christians can point to their saints who wrote the New Testament, just as the Jews can point to the prophets in turn. If Satan exists, the weight of the evidence seems to support Judaism on this issue.
Which raises the secular view that Satan does not even exist, and therefore does not need saving. After all, Satan was never mentioned in any book written before the Babylonian Exile, when the notion of Satan may have been received by the Jews from their Persian benefactors.
As far as we know Lucifer does not have a son. Lucifer is a spiritual being and they do not procreate.
Lucifer has the power of illusion.
Lucifer is a fallen angel.
No, Freemasons don't love Lucifer.
Hendrick Lucifer was born in 1583.
Lucifer means Light-bearer.
The Flight to Lucifer was created in 1979.
Lucifer's Hammer was created in 1977.
None But Lucifer was created in 2002.
The ISBN of The Lucifer Principle is 9780871135322.
Lucifer - band - was created in 1999.
Lucifer Sam was created in 1967.