One explanation for legal proceedings that makes sense in this scenario is that Carlson might have to stay off the air entirely for the next three years while he collects his $60M. He may be looking for legal avenues to buy out the contract so he can get paid more than $20M/year to work for someone else immediately.
Tuckers contract expires at the end of this year. Only 7 months of paychecks left if Fox didn’t terminate him for cause. The fact he hired this lawyer suggest Fox terminated him for cause.