Ideally whenever a Sales Activity is posted against a lead, and if the below setting is in place, the lead's stage should change to the Final stage set up in a particular account( e.g. Customer )
However, if you come across an issue wherein a non-Admin user (Sales User/Sales Manager or a Marketing User) adds up a Sales activity and the Lead stage does not get changed, you can check if under Settings--> Users and Permissions--> Permission templates--> Sales User Permission( as was the case in this scenario)-->Actions-->Edit-->Lead Stage is restricted to be Edited by that User or not (PFB):
Conclusion: If yes, then the Lead Stage change will not happen upon posting of a Sales activity by any Sales User.
Work-around/ Resolution: If the requirement is to restrict the users from changing the Lead Stage from their respective logins and still it is wanted that that the Lead Stage be updated whenever a Sales activity is added, the Admin can create a rule under Rules and Notification stating whenever a sales activity is added--> Update the Lead Stage to Final Stage.