Let's recap. This is my current understanding:
The app is deployed with the FE on each workstation, and an Access BE on the server. Server permissions have been checked and are OK.
Sometimes without rhyme or reason some user gets the "currently locked" message.
I am not convinced yet that there is an issue. It is normal in a multiuser application that this message or similar ones happen. Often a well-designed error handler can deal with it (e.g. by going to sleep for 100 msec and trying again). Of course a lot depends on many finer points of your implementation. For example there are properties at the form level that affect how records are locked.
It is good to understand that 2 users do not have to be saving the SAME record. Access saves a memory page at a time, and such 4K page may contain several records.
Also, can you confirm that all users are on the same version of Office and all updates have been run? What is that version?
-Tom. Microsoft Access MVP