Lookup relationship field: auto-populate ticket field with data from lookup user/object

Hi all. I'm usually able to figure out just about anything on my own, but I'm struggling with this one and could use some help!

If I'm using a lookup relationship field in a ticket form, I would like to create trigger that automatically populates a ticket field with an attribute from the related object. Here are some use cases:

A - A user requests a piece of software. The Agent selects the application's custom object, and I want the name of the approver to be copied into the "Approver" field. 

B - I have a Requested For field (this is used for when the Requester is different than the person the request is for) and it is a lookup field that points to customer records. I would like the Email address of the Requested For user to be copied into a dedicated ticket field, and would like the user ID to be copied into a hidden field. 

C - Employee Onboarding. I would like the manager to be the Requester, and I would like the New Hire to be a lookup field that links to a customer record. I would like all of the New Hire's employee details (in custom user fields) to be copied into fields on the ticket form. 

There are several more use cases that I would like to use this functionality for, but the key piece that's missing for me is "How do I set up a trigger that goes and grabs data from a related object field and copy it into a ticket field?". I should also state that I am comfortable with webhook and JSON, but would prefer to accomplish this without using a third-party app. I'm already spending close to $20k on apps to fill in the gaps of Zendesk functionality. 

Thanks in advance!

- CJ