The story you heard about a lawyer avoiding discipline because the state Supreme Court justices recused themselves is not what they are saying it is...

 The headline in Above the Law reads: "Convicted Lawyer Too Well-Connected To Face Discipline".  Elsewhere, the story was reported as "After most Illinois Supreme Court justices recuse themselves, Ed Burke keeps his law license".   The ABA Journal reported the story as "Convicted alderman keeps law license after recusals prevent state supreme court from acting."  You may have heard or or read something like that somewhere else, but the full story is not what it seems.

These headlines suggest that a convicted lawyer could not be disciplined even though he was convicted of a crime.  But that is not necessarily the case.  What happened is that the Disciplinary Agency asked the Supreme Court of the state for an interim suspension because he was convicted of a crime.  "Interim" means that the suspension would be in effect while the Agency decides the disciplinary case.  Some justices in the Court recused themselves and there were not enough justices left (following the state constitution) to grant the petition.

This does not mean that the lawyer will not be disciplined, or that he will avoid discipline.  The lawyer will avoid a suspension while it is decided whether he will be disciplined, but that is a different thing.  It may very well be that the disciplinary agency decides to impose discipline -- in fact, it is possible the agency will decide to disbar the lawyer.   

Now, what happens after that, I don't know.  If the disciplinary agency disbars the attorney, he then has the right to appeal to the state's supreme court.  If the same justices who recused themselves regarding the interim petition recuse themselves from the appeal, the court can't hear the appeal.  Does that end the case and the decision of the disciplinary agency stands?  That's my guess, but I have not looked into it.