Well, it could be that the man is an old wizard who has some important information to pass on to Harry. In order to do this in a very old - fashioned and perhaps superstitious way, he asks Harry to sit on his lap. Harry is initially reluctant but then realizes the importance of the information and complies. The story could then be about how Harry uses this new knowledge to solve a mystery at Hogwarts.
The man could be a magical creature in disguise. He forces Harry to sit on his lap because he needs Harry's help. He can't communicate properly in his normal form, so by having Harry close like this, he can transfer his thoughts directly into Harry's mind. Harry then has to figure out what the creature wants and how he can assist it, all while dealing with the awkwardness of sitting on the 'lap' of what he thought was a strange man.