According to LDS Bible Dictionary, the Laban in OT:
Laban
Son of Bethuel, grandson of Nahor, grandnephew of Abraham, brother of Rebekah, and father of Leah and Rachel. His branch of the family remained at Haran when Abraham moved on into Canaan. The dealings between the two branches are described in Gen. 24; 27:43–31:55. Jacob lived with him and served him for 20 years. There was a good deal of mutual deception, each trying to outdo the other; but the final parting among the mountains of Gilead was a friendly one.
According to LDS Triple Combination Index, the Laban of BOM:
Laban—custodian of brass plates [c. 600 B.C.]
has record of Jews: 1 Ne. 3:3 . sons of Lehi1 sent to get records from: 1 Ne. 3:4–11 . refuses to give up record: 1 Ne. 3:12–14 . takes sons’ property without giving plates of brass: 1 Ne. 3:25–26 . to be delivered into sons’ hands: 1 Ne. 3:29–4:3 . is slain by Nephi1: 1 Ne. 4:7–18 . sword of: 1 Ne. 4:9, 18–19, 21 . ( 2 Ne. 5:14 ; Jacob 1:10 ; W of M 1:13 ; Mosiah 1:16 . ) descendant of Joseph1: 1 Ne. 5:16 .
Laban in the OT is Jacob's father-in-law (and his uncle) who tricks him into marrying the wrong daughter and tricks him into working and extra 7 years in order to marry the RIGHT daughter. That is BEFORE the sojourn in Egypt.
Laban in the Book of Mormon is one of Nephi's brothers who leaves Jerusalem at the beginning of the Babylonian captivity which is around 1000 years later.
I think it was Krakauer in his book "Under The Banner of Heaven" that made the mistake of identifying the Laban in the Book of Mormon as being the same Laban that was in the Bible.
They are quite different, as other posters have said.
You're right, it was Krakauer, and he admitted he made a mistake there. However, given everything else he got right, I'm willing to cut him some slack.