This question has been answered by BobRay. See the first response.
In order for users to see resources in the tree, they need a Context Access ACL entry for each front-end context (e.g., 'web') in addition to the one you gave them for 'mgr'.
They'll also need resource_tree, file_tree, and element_tree permissions and probably 'load' and 'list' permission.
You might try using the "Load, List, and View, Policy for all ACL entries and see what that gets you.

On the Permissions -> Context Access tab, add two new entries to the grid:
Context: 'mgr' Minimum Role: 'Editor', Access Policy 'AdminLite'
Context: 'mgr' Minimum Role: 'Editor', Access Policy 'Load, List and View'
Context: 'web' Minimum Role: 'Editor', Access Policy 'Load, List and View'The problem is that without edit permission, they can't always see the actual content of the objects.
You might try giving them everything but save_document, save_template, save_chunk, etc., or just not give them basic 'save' permission. That way they can see (and edit) everything but can't change anything permanently.
Did you remove the save_document, etc. permissions, or just 'save'?
If you want to, you can edit the lexicon entry that gives the "Access Denied" message (or whatever you're seeing) to say something else.