Here's an excerpt from the Wikipedia link:
Luluwa (also Aclima) according to some religious traditions was the oldest daughter of Adam and Eve, the twin sister of Cain and wife of Abel. According to these traditions, she was the first female human who was born naturally. According to Islamic and rabbinic tradition, a marriage between Luluwa and Abel was proposed and arranged by their father Adam. In order to commence contentment from Luluwa's twin brother, Adam (their father) suggested that a sacrifice be made, yet sacrifice was subsequently rejected by God. The reason behind the commotion was that Cain viewed Luluwa as being aesthetically more attractive than Awan.
No, Cain didn't. Just because someone comes up with a fabricated story doesn't mean that interpretation has any legitimacy. Luluwa is not part of the biblical story. If you want to know what the Bible says, then we have to look at what the Bible says, and not what someone has added to it.
Adam and Eve chose to take wisdom (the "knowledge of good and evil") for themselves, making themself the source of order and wisdom. Genesis 4-11 shows that all attempts by humans to be the source of order and wisdom were unsuccessful. Even religion, cities, and civilization do not, in fact, lead to an ordered, wise, and godly condition. Genesis 12 then begins the story of God showing what will lead humanity there, and it's the divine-centered covenant.
Genesis 4 shows that sin continues and increases. It shows the first of many evidences of how desperately the covenant (and God's intervention) is needed. It shows what the world looks like under the reign of sin and death. It shows why God had to enact a plan to restore what was marred.
In other words, to see Cain as killing able over his sister doesn't fit the template. It's an obvious fabricated insertion. Rather, the story of Cain and Abel is about the issue of an offering to the Lord (Gn. 4.3-4) and the value of retaining God's favor. When God removed Adam & Eve from the Garden, their true loss was not the Garden, but instead God's presence. Genesis 4 follows that story, as Cain and Abel are shown seeking God's presence with their offerings. Sacrifice is a relationship-building activity. Cain's sacrifice was given grudgingly instead of with honor (v. 5), and therefore it won't accomplish the purpose of motivating God's presence. Cain was trying to approach God on his own terms, just as Adam and Eve had done. That's the point. To twist it into wanting Abel's twin sister is just an untenable mutilation of the text.