I can't recall a time when Purdue has ever fired a coach in the middle of the season. If true, which I doubt, it would mark a significant change in Purdue's strategy towards athletics.
No, Purdue is NOT LSU. LSU fired their coach because they wanted to get rid of him, had already made up their minds after they realized the season wasn't going to be what they wanted and fired him before he could save it by going 9-3 or 10-2.
That being said, there's a number of reasons a school like Purdue would want to make a change early in the situation they are in.
1. They likely know they aren't going to bring back Hazell, and quite frankly even if we won 6 games. It's not just wins/losses that's a problem, it's recruiting. Recruiting is foreshadowing of the future - you could bring in the best coaching staff in the country and we could only do so much with the lack of talent, and particularly depth, that Purdue has. It's no secret that Purdue needed a new AD in place prior to firing Hazell. Purdue botched this situation by being so reactive (basically throwing this season out the window).
2. With a new AD, this will obviously be one of his first impressions on Purdue fans and you want this to be a positve start with a positive hire. Knowing this change will likely take place, you want to get started.
3. You can't get started on hiring a new coach unless you have really gotten rid of the one you're replacing. You can do some back channel things, but it's rather minimal. For example, you can hire a firm to start putting out feelers - but if you're trying to beef up a salary pool, you probably can't start going to people about that while you still have a head coach - if that leaks, it's a bad situation. If you fire a coach, it frees you up to do anything you need to to lobby, fundraise, etc.
4. With a school like Purdue, it needs to do these things to hire competitively. If we wait until after the last game of the season, we'll be behind the eight ball as several schools will be several steps ahead of us. Purdue's hardly an unattractive job, but we have a lot of competition on the level we are at - so if even 2-3 schools are in better positions than we are in hiring a coach, that's a big disadvantage for us. The earlier you can start this process is better. It certainly doesn't guarantee anything - Maryland fired Edsall in October and didn't hire Durkin until after regular seasons ended. However, they had already gone through their 'dream' candidates and other top candidates and hired someone within a few days after the rest of the schools had just finished their regular seasons.