Additionally, add the External Lawyer Contact as a Contact Participant on the Matter associated to (if not already done so) for additional tracking.
Setup a Contact

Setup a contact for the <'External Lawyer'> (if not already available in your system).
Create a Timekeeper for <'External Lawyer'>

Choose the contact that has been setup in your system to represent the <'External Lawyer'> who performed work to create a distinct Timekeeper record for them.
Create a Billing
Change the Timekeeper field to <'External Lawyer'>
Set Rate Type field to 'Staff Rate' to show this Timekeeper's unique rate amount
Finish billing as needed.
Click Save
Suggested Additional Steps to ensure proper tracking and Association:
Add the <'External Lawyer'> as a Contact Participant on the Matter associated to (if not already done so).