A Chicago neurosurgeon owes $2.2 million in damages for trying to defraud his next-door neighbor.A Cook County jury on Monday awarded the estate of Virginia “Ginny” Rogers damages against Dr. George Dohrmann III.Dohrmann initially sued Rogers’ estate in 2007 trying to enforce a contract that would have awarded him Rogers’ large Lake Shore Drive apartment and $4 million in cash upon her death. Her …