The Veterans Affairs Department has agreed to pay up to $20 million to veterans for exposing them to possible identity theft in 2006 after losing their sensitive personal information. In court filings Tuesday, lawyers for the VA and the veterans said they had reached agreement to settle the veterans’ lawsuit alleging invasion of privacy. The money will be used to pay for veterans who suffered actual harm, such as emotional distress or expenses incurred for credit monitoring. The lawsuit came after a VA data analyst in 2006 admitted that he had lost a laptop and external drive containing the names, birth dates and Social Security numbers of up to 26.5 million veterans and active-duty troops. The laptop was later recovered intact.