First, I don't trust Jim when he makes such an open or bald statement. Jim will mislead us if he thinks it will make the story read better; be more dramatic, when we finally get our hands on it. Now, that doesn't mean that I think that the entire statement was a lie. I won't be surprised, in fact I expect, that Harry will be upset when he learns about the details of Lea and Margaret's deal, but he will probably be most upset by how Lea interpreted the rules that governed her behavior after Margaret's death.
There is no way to be certain about this, but it could involve Lea looking the other way while Malcolm Dresden was murdered and perhaps making a deal with his killer because she judged that Malcolm Dresden was incapable of teaching Harry or guarding him while he was a child. In this version of events Margaret failed to include protection for her husband as part of her deal because he wasn't a player in the supernatural world and normally wouldn't have been targeted. My reason for this guess is that Jim has also stated that Margaret Le Fae didn't make the best deal she could have made.
The above paragraph is just one possibility, there could be others. Imagine if Margaret's deal for protection included any grandchildren, if the parents couldn't protect them. Harry becoming engaged to Lara might make Lea believe that the clause of protection for little Maggie was know operational. I don't think Harry would react well if he found out his Godmother was also his daughter's Godmother, but I digress. Harry throwing down with Lea could be a verbal exchange leading to Harry trying to out maneuver Lea, leading to a brief violent confrontation broken up by Mab or by an enemy attacking both of them or Harry coming to his senses and realizing that he needs to control his anger. Just because Jim says that Harry will throw down with Lea doesn't mean it will become a fight to the finish.