Yes and No. Lead Liaison will allow you to make multiple copies of a contact list using the Copy function under Contact Lists --> View Contact Lists. Unfortunately, this feature will only carry over custom field associations and other details, but will NOT copy over subscriber data.
The proper way to transfer subscriber data across multiple contact lists is by using the Import/Export from File functions. By default, export will only move active subscribers, so if you also want unsubscribed/bounced subscriber data to carry across to your new list, ensure you use the "Search for contacts to export from my contact list" option, and set Activity Status to "Any".