A lookup field in a custom object needs to be updated after the record is submitted for approval and locked.
Is the trigger able to achieve this, even if the record is locked?
The answer is, it depends.
If you have your code written directly in the trigger or in a class designated
If you use code in a class marked
It is if the user is ;)
If the action is initiated by System Administrator - sure. Otherwise - tough luck, exception will be thrown. It also depends if you've configured the approval process to "Administrator or current approver can edit the records".