Cain's offering was the fruit of his own labour from the ground that had been cursed after the fall, which was not acceptable to God. As a result he got angry, killed his brother and ' went away from the presence of the Lord'.
Abel's offering was a slain animal, the firstlings of his flock, which was acceptable to God. 'Abel' means 'breath' which signifies spiritual man.
In Cain is exemplified the religion of the natural man, who will approach God with offerings of a natural kind, whilst in Abel is exemplified the worship of the spiritual man who will approach God with the offerings of the slain lamb, offerings of a spiritual kind.
Lucifer, spoken of in Isaiah ch.14 vs 1-20, is a name signifying in Latin 'Light bringer' or 'light bearer', which was given in irony to the king of Babylon because, in his pride, he said he would exalt his throne above the stars of God. He was the oppressor of God's people, allowed into Heaven, though human, a 'light bearer' cut down and fallen from Heaven because he destroyed his land and slew his people. Babylon was where God's people experienced a mixture of God's teaching and man's teaching. the name reflects the word Babel, which means 'confusion'. Christians, though 'seated in Heavenly places', can be in spiritual Babylon when they mix God's pure teaching from His word with mans' doctrine. the only thing acceptable to God is Jesus, the Word of God, the slain lamb. The fruit of our own labour, our own works, have no standing with God whatsoever.