Does the current 2 year statute of limitations (on consumer debt) also include money a lawyer claims he owes you?

Yes, provided that the debt was incurred after January 1, 2004.

Not that it has any effect on the limitation period question you asked but you said the lawyer claims HE owes YOU money. If you meant that he claims YOU owe HIM money, presumably for a bill, then our comment stands.

If, however, the lawyer owes you money it may be a matter for the law society regardless if the limitation period has expired.