I have been using Acrobat Pro DC for some time and was able to open a PDF from OneNote, Edit and then save back to OneNote. Now I get the following message "The document could not be saved. The file may be read-only, or another user may have it open. Please save the document with a different name or in a different folder."
As per the issue description mentioned above, you are getting The file may be read-only, or another user may have it open message when trying to save a pdf opened from one note, is that correct?
Could you check if you have preview pane and details view enabled (if using Windows)in Windows Explorer? If yes, try turning them both off and try again? Does that work?
If not, try whitelisting the network path (if the pdf is located on a network drive) using the steps given below:
Click Edit>Preferences>Security(Enhanced) , choose Add Folder path.
Relaunch Acrobat and try again.
You may also refer to the following forum thread discussing the similar issue:
Also, let us know dot version of Acrobat and the operating system installed on the machine? You may refer to the steps given in this link on how to check the version in Acrobat: Identify the product and its version for Acrobat and Reader DC
Let us know if you need any help.