The Inspector General should invistigate anyone who seems suspicious or might have information regarding the case. This does not mean that the IG should assume she is guilty or hiding something, just that she may or may not have relevant information that she has not been forthcoming about, and could be uncovered in an investigation.
Attorney General Loretta Lynch, as part of her role as head of the Justice Department, overseas the FBI. The FBI is conducting an ongoing investigation into whether or not Hillary Clinton broke any laws by using a private email server. Lynch's meeting with Bill Clinton appears to be a conflict of interests to many; because Lynch will be perceived as being biased in her investigation. Therefore, the Inspector General should investigate Loretta Lynch to see if her meeting with Clinton was inappropriate.
Yes, Loretta Lynch should be investigated by the inspector general. Her meeting with Bill Clinton has made her and her department biased towards the proceedings of Hillary Clinton's email scandals. No further investigation should be done until the inspector general has made sure that Loretta Lynch is fully capable of continuing the case.
No, there is no reason for Loretta Lynch to be investigated by the Inspector General. There is no indication that Lynch has handled her job as the attorney general in an inappropriate manner, either before or during the investigation into Hillary Clinton's tenure as secretary of state under President Obama.