Using Git requires a change in thinking.
All authors need to abandon the thoughts of 'check out', 'check in', 'lock'. Those don't really apply to git.
New concepts that are absolutely essential to learn are 'remote', 'origin', 'branch'.
When an author pulls a repository ( pulling a copy of the main repository), they are creating a local repository. Their work will take place in this repository. Usually, good practice is to create a local branch for new work. *Always* update your local repository before starting a new piece of work (fetch and pull the latest updates from the origin).
When working on DITA files, the files are numerous and small. It is unusual for two authors to both edit the same file at the same time. Frequent updates and pushes are the way to work.
This is no different to programmers working on code.