He's a defensive minded head-coach that had one of the worst defenses in the NFL this season, on one of the easiest schedules (looking at SOS) in franchise history. TB was allowing the league worst 70% completion % allowed per game, was ranked near the bottom for TDs allowed, was ranked near the bottom for YPA, was ranked near the bottom for INTs, 2nd worst defense for QB rating, etc. And this was after a disastrous 2014 season on defense as well.
Moreover, TB was one of the worst (if not the worst) penalized team in the league. Discipline on the field is definitely on the HC.
To only get 4 more wins than last year, which you could argue is because of a new OC and a potentially good QB is the main reason for his dismissal. I think ownership/GM were worried about breaking up the offensive continuity because teams were interviewing Koetter, and this will eventually play out with either making Koetter HC, or bringing in someone like Koetter as HC to keep up the development of Winston.
I can understand for non-Bucs fans how this will look like a boneheaded move, but watching the games you can see that Lovie really wasn't the reason for this years improvement. That improvement was on the OC/QB, which he doesn't coach.