Isopods are crustaceans, like crabs and lobsters. And like crabs and lobsters, isopods originated in the oceans and then evolved to become terrestrial. In fact, they have become so successful on terra firma that, according to Brusca, there are more terrestrial isopod species than there are marine species. It seems that they are now on their way up the tree trunks. If they face a strong enough selective pressure, who knows, maybe one day they will even evolve wings to conquer the skies.
During my recent trip to Antwerp, Belgium, I encountered these isopods on wet tree trunks late in the afternoon after a rainy day in a wooded park. I was actually looking for slugs; instead, I found isopods. According to the notes I took, they were on both smooth- and rough-barked trees. The highest ones I saw were more than 2 meters above the ground. As you can see in the pictures, the tree barks were covered with green algae (cyanobacteria) and probably also with fungi. I suspect the isopods were partaking of the algae and the fungi.
So, if they were feeding on the trees, then the answer to the question posed in the title of this post is Yes, isopods grow on trees.
I don't know anything about isopod taxonomy, but based on the patterns and colors visible on their dorsal surfaces (the technical term for that part of their bodies is pereon), there were at least 3 species.
And this one:
Of course, they may all be the same species and the observed pattern and color differences may be due to age, male-female dimorphism or polymorphism, etc.
Isopods were featured on this blog before in this post and in this post.