Wait, what's the contradiction? You can definitely have liberal fascism. Italy under Mussolini is considered by many scholars as a liberal, fascist regime. There's lots of scholarly work on the subject.
What scholarly works are you referring to? I can only find one book and it is misusing "liberal" as a synonym for "left-wing". Left-wing authoritarianism is not inherently contradictory, but liberal authoritarianism is.