My understanding is that Joe Banner, who was Haslam's first hire last fall, has final authority on football operations. He actually worked with Lombardi in Philly back in the late-90s, so I think he probably had him top of mind when he was initially cleaning house after last season, even though Chud was technically hired first.
I'd guess Haslam was frustrated and looking to make a statement after the team fell apart down the stretch and Chud was an easy scapegoat that Banner was willing to go along with (we saw a similar reflex from Shad Kahn in JAX last season, firing Mularkey after one year). Of course, Banner can always throw Lombardi under the bus down the road to buy more time for himself.