The 33-year old had a third operation on Thursday to try and resolve the groin and hip injury that occurred at the European Championship.
It is likely that Dunne will miss Ireland's games with Sweden and Austria in the New Year and Lambert admitted he was hopeful the defender was finally on the road to recovery.
"Richard has had the operation in America and we are all hoping that once and for all it will be cleared up," Lambert told the Irish Examiner .
"This was the only place where we could get it done.
"He will come back over from the States in the next few days and hopefully start his rehab and then begin to look to the future.
"I’ve never seen anything like this and the medical people have never seen anything like this either. We have got to hope it has now been cleared up by this operation.
"The original injury occurred at the Euros and sometimes you can get to the bottom of it quickly and on other occasions it takes longer than you think.
"As a footballer you get frustrated because you cannot put your finger on the problem."
Lambert confirmed Villa was not seeking compensation and added: "We have not been down that road. Injuries can happen to players."