Are all Hermitian Lorentz-invariant Lagrangians CPT-invariant?

[Breo]

Are all the hermitian and lorentz invariant lagrangians, invariant under the combination of CPT?

If yes, how can it be proved?

 

[ChrisVer]

http://users.ox.ac.uk/~mert2255/papers/cpt.pdf

Here is a rigorous proof of the CPT-theorem...
In a general framework, Lorentz invariance is not needed for CPT symmetry to exist. Neither the violation of CPT would necessarily mean the violation of Lorentz invariance.