I think that Lyon probably shouldn’t be in the Test team except in Asia.
He isn’t as good a spinner as any of the four main quicks are at their role, and he is keeping Pattinson out of the team.
If Australia had a good spin-bowling all-rounder, or a keeper who could bat at 6, then Lyon wouldn’t be in the team. A Jadeja or a Watling would make him unselectable.
I think that if Australia had Pattinson batting at 8, Cummins at 9, Starc at 10 and Hazlewood at 11 they would have a West Indies 76-95 quality attack.
But that would require a Carey batting at 6 and a Jadeja or even a Moeen Ali batting at 7. And that Aussie Jadeja does not exist.