The best grifters always find their marks, or the people they are certain can be taken advantage of, and when they do, their scams can't help but succeed. Lingk is Roma's mark.
Mamet leaves Lingk as a bit of a mystery, and we don't really know much about him other than he has a wife that calls the shots. He buys into Roma's pitch and takes a risk, but in the end he doesn't have the power to make his own decisions. He comes to the office and tells Roma he has to back out of the deal, but he wants Roma to know that it's not his fault:
LINGK: I don't have the power. (Pause.) I said it. (2.1.872)
Even after the deal is bust—even after Lingk knows that Roma has been lying to him—he still feels bad for what he's doing. This is his last line:
LINGK: Forgive me. (2.1.948)
Other than the cop, Lingk is the only character in the play who does not live in the world of the office. He is a different type of man than Roma or Moss or Levene or Williamson, and because of this he allows the audience to see what these guys (specifically Roma and Levene) think of their clients and how willing they are to manipulate other people in order to get what they want.
There's something interesting about Lingk that shouldn't be overlooked, though. The fact that he succumbs to the wishes of his wife (she supposedly demands that he cancel the contract) paints him as the only person in this play who isn't simply out for himself. While the others may view this as weakness—and Lingk might agree with them—the decision he makes to back out of the deal is most likely the right one to make. We see a man who doesn't simply live for himself, and in the end, that saves him from getting fully drawn into the world of Roma and the others.