Hello szhu0,
[R] mark next to the chunk's label in the Workspace pane means that the chunk is Referenced in either local or geographic coordinate system. This mark has nothing to do with the project lock that makes opened project read-only for other user or other application instances that are trying to open the project.
Have you tried to export anything from the project? Actually, even if you open the project in read-only mode, you still will be able to export the results, as they do not affect the project files data.