I've created a custom formula field on the Lead object named 'Lead Division Region' (for reporting purposes) and its set equal to the $User.Division. The issue I'm having is when the Lead changes owners it doesn't update the field to the new owner. I tried using the Process builder for this but it won't let me update the field. Any ideas on what I could do to update this field to the new owner's division? And it would be great if someone could explain why it isn't updating the field in the first place. As always thanks for the help!
$User is the current viewing user, not the owner.
Since owner is a polymorphic field on Lead (it can be a User or a Queue), try:
If you are using queues for leads, you'll need to check whether the owner is a Queue or User first, so you'd something like this instead (returns the Name instead of Division for the Queue):
IF( ISBLANK(Owner:Queue.Id), Owner:User.Division, Owner:Queue.QueueName )