Can I place a lien on a law firm that owes me money?

Do you have a judgment against the law firm?  In most cases, you cannot "place a lien" just because you say someone owes you money.  You have to sue that person (in this case the law firm) and win your case.  Once you do that, you can (assuming they don't pay you what the Court finds that they owe) take steps to collect the money they owe, such as collecting it from their assets either directly (if the assets are money, such as a bank account) or having the assets sold (if it is property, such as a computer) and collecting from the proceeds of the sale.  I'm oversimplifying a bit; you can't just walk into a bank and demand the money from their account or seize their property and sell it, but the point is that you must go to court (or to arbitration if your contract with the law firm has an arbitration provision), you can't simply help yourself to money they claim you have no right to.  In rare cases, the Court may allow you to restrain the law firm's assets even before a judgment is rendered (generally requiring you to post a bond to reimburse the law firm for any damages this causes if it turns out you don't win your case), but it seems likely that, in the case you describe, you would not be able to do so until and unless you win the case (unless you agree to a settlement with the law firm).