(Adapted from 'Otzar Ishei haTanach)
Lavan was born on the merit of Avrohom. Like her sister Sarah, Milkah (mother of Besuel, Lavan's father) was barren, and it was only when Sarah became pregnant, and G-d cured all the barren women, that she became pregnant too (Medrash haGadol).
The Torah relates that Avrohom sent his children, the sons of Keturah (alias Hagar) to 'the land of the east', and that he handed them 'the impure name' (incorporating the ability to perform witchcraft [see Rashi Chayei Sarah, 25:6]). And it is from that land that Lavan, Beor and Bilaam came (Zohar).
When Lavan chased after Yaacov, he had no intention of doing battle with him, since Yaacov's forces were far stronger than his. What he wanted was to kill him verbally (i.e. through witchcraft [Zohar])
That explains why, when G-d appeared to him, He warned him not to speak with Yaacov good or bad (rather than not to fight him).
Lavan (Beor) was alias Bilaam and Kushan Rish'asayim (king of Aram). He was called Be'or - because he had relations with his ass, and Bia'am - because he attempted to swallow the people (of G-d ['bola am']), and Kushan Rishasayim - because he perpetrated two evil deeds: He desecrated the oath that he took not to cross the pile of stones (that he together with Yaacov. had erected to mark the peace-treaty that they established) to harm the descendents of Yaacov, and he subjugated Yisrael for eight years (Gemara Sanhedrin and Yerushalmi).
Kushan Rish'asayim was unlikely to have actually been Lavan however, since five hundred years separated them; Moreover, he cannot have been Bilaam, whose death is recorded in Matos. What Chazal must therefore mean is that the one was a Gilgul (a reincarnation) of the other, as the Yaavetz explains.
Likewise, Bilaam became lame when, on his way to try and curse Yisrael, he squeezed past a stone wall (made from that same pile of stones), squashing his leg in the process (Targum Yonasan), thereby abrogating his oath.
Lavan was alias Kemuel ("the father of Aram"), which is the acronym of 'kam neged umoso shel Keil' (he arose against G-d's chosen nation). Medrash Rabah.
When Yitzchak instructed Yaacov to travel to Aram and take himself a wife from the daughters of Lavan he did not yet have any children. But the moment the Tzadik Yitzchak uttered the words "from the daughters of Lavan", Lavan's wife conceived Rachel and Leah (Medrash Rabah, in contrast to the previous Medrash).
At the same time that Rivkah gave birth to Eisav and Yaacov, Lavan's wife gave birth to Leah and Rachel. In an exchange of letters, it was agreed that Eisav (the older twin) would marry Leah (the older twin) and that Yaacov would marry Rachel. (See Rashi Vayeitzei, 29:17). (Medrash Tanchuma)
Before Yaacov arrived in Aram, Lavan had no sons. It was only on the merit of Yaacov that his wife subsequently bore him sons (Medrash Rabah).
Yaacov informed Rachel that if her father Lavan was a trickster, he was his equal in the art of swindling (Gemara Megilah) This teaches us that one does not handle a trickster in the same way as one deals with an honest person (as David haMelech wrote in Tehilim).
The camels of Avrohom refused to enter Lavan's house until he had cleared out every vestige of idolatry (Avos de'Rebbi Nasan).
Note that there are two countries by the name of Aram - Aram Naharayim (Avrohom's birthplace) and Aram Tzovah (Syria). Aram in the above article refers to Aram Naharayim.
