Because Clinton is running for president it is pertinent that all meetings and all communications be monitored so that the public can make an educated and well thought out decision when voting time comes. Though it may not be necessary to disclose the content of the meeting, it should be investigate to make sure that everything is on the up and up.
No, the Inspector General should not investigate Loretta Lynch over her meeting with Bill Clinton. Lynch has publicly stated that she will defer to the FBI and follow whatever recommendations it makes when it concludes its investigation into Hillary Clinton's handling of her emails. If Lynch goes against the FBI, then an investigation might be warranted then, but it is not necessary at this point.
According to the news articles, they say that former President Clinton unexpectedly ran into Loretta Lynch and it was not a planned meeting. No one really knows what the discussion was about, and people need to trust that Ms. Lynch will uphold her civic duty and have the integrity to make the right decision.
It's crazy how people are getting so bent out of shape about this. The two people met, in private, and no one knows exactly what they talked about. There is nothing that this one meeting can do to cover up evidence or protect a person for prosecution. There might have been talks of certain issues, but nothing can really change the outcome without public outcry.