Hi,
You can also use Relationship Mapping to populate fields from Parent to Child Entities.
For instance, when you qualify a Lead, data is copied to created account and contact automatically (Address State as well).
In your scenario, Lead address is being copied to related account and contact.
You can add or update fields to the mapping, for instance for populating a filed value on Contact from Originating Lead:
- Go to System Settings -> Customization -> Customize this System.
- Expand Entities, select Lead Entity.
- Click on 1:N Relationships.
- Double-click on Lead - Contact relationship.

- Now you see existing fields mapped, and you can also add new:

Please note, this only works when you create a child record form Parent records form.
For more advanced scenarios,as suggested by others, you can use flows, workflows and plugins.
Best,
Wahaj