The more I observe LSU in 2015, the more the situation reminds me of UT in the mid 00s. You have a national championship winning coach who is starting to slip a little bit, but who is still winning most of the time. LSU's Athletic Department is arguably one of the worst run in the SEC; not that different from our AD under Hamilton. Chavis left mostly due to the AD; not Les Miles.
If LSU fires Miles after a 9-3 season, it might be tricky getting a top-notch coach to replace him. Even though the LSU job is easily one of the best in the nation, who wants to walk into a situation where 9-3 gets you fired? And with so many other potential openings, it might be more attractive to take a slightly lower salary and less prestige to go coach somewhere like Virginia Tech than deal with completely unrealistic expectations at LSU.
Here's the thing: there are very few "home run hires" in the world of college football. In the past two decades, the only "home run hires" were Nick Saban at Alabama and Jim Harbaugh at Michigan. Every other hire carried significant risk. We've seen plenty of coaches succeed at one level and then completely fail at a top-tier program. We've even seen coaches have great success at a major conference program and then fail at another major conference job where there's more pressure (see RichRod at Michigan).
LSU may well get lucky and attract a top-caliber coach. But if they fire Les Miles after going 9-3 or even 8-4, it's far from a given.