Greg Sargent explains how it would work:
Lieberman's law would amend an earlier statute that details other things that can cost you citizenship: Serving in the army of a foreign state, pledging allegiance to a foreign state, and so on. In those cases the State Department decides whether your disloyalty merits loss of citizen status. Lieberman's law would add involvement with a foreign terror organization -- as opposed to a foreign state -- to this list. ...
Who would determine whether you're involved with a foreign terror group? The State Department. It already decides what is and isn't designated as a terror organization. Lieberman's law would also empower State to determine whether you are in league with one of these groups.
Here's where it gets more complicated. You would still have the right to contest this in court. And if you did, the burden of proof would be on State -- not on you -- to persuade the court that your involvement with a terror organization is sufficient to justify taking away your citizen status.
Bottom line: Lieberman's law can't keep you out of court against your will if you want to contest efforts to strip your citizenship. And chances are that if you were already facing other charges -- plotting or executing a terrorist act -- you would be simultaneously tried for that in civilian court, too, even as State continued to try to revoke your citizen status.
Sargent notes that Chuck Schumer has come out against Lieberman's proposal.
Does that mean Schumer is also opposed to the current statute that allows the State Department to strip the citizenship of those working for a foreign state, but not a foreign terrorist organization? It seems to follow that if you oppose one you should oppose the other.