re: How easy is it for tthe Governor remove an LSU president?

Alleva CAN be Fired for Cause:

A few important terms of ALLEVA'S contract with LSU below:

2. Duties and Responsibilities:
A. Administering, managing, and leading the Department of Athletics at LSU A&M (the Department) in such a manner as to reflect positively on LSU at ALL TIMES.
B. Administering, managing, and leading the Department in such a manner as to allow its athletic teams to effectively compete in National Collegiate Athletic Association (NCAA) play.

9. Termination: This Agreement may be terminated by the parties as follows:
A. Termination by LSU for Cause.
2. Commission of Material Violation
(i) the violation occurs or continues to occur after ALLEVA knew or should have known that it was about to occur or was occurring
4. Knowingly engaging in conduct which:
(i) displays a continual, serious disrespect or disregard for the mission of LSU
(ii) brings ALLEVA or LSU into public disrepute, or negatively impacts the reputation of LSU