If you go into the roles for the actaul Planning application you will see 'Essbase Write Access'. Give them that and Server Access.
Do you know they can also open your Planning Forms in Smart View?
I gave them exactly what you wrote and made refresh security. Afterwards I checked and I got Essbase Error (1020043): You do not have sufficient access to perform a lock on this database. Yes, they can also open Planning Forms
1) Open the specific Excel spreadsheet
2) Select “Essbase > Options” from the Essbase Excel Add-In menu
3) Select the “Mode” tab in the Essbase Options window
4) Check the “Update Mode” box
5) Select “OK”
6) Save the Excel spreadsheet
I don't work with Excel Add-In menu, but with Smart View (Ad-Hoc Analysis), there is no lock and send method here, but submit data. Anyway, it seems that the source of the problem is not in Smart View, but in Shared Services.