The customer would want that data to be pulled into SharePoint LMS for each user. Does it make sense? Can we accommodate them?
Yes this is possible and as part of the SharePoint Server it can be solved using the OOB Business Data Connectivity service application.
You can import data from SQL server, and use that data to add properties to existing user profiles. During this phase, you create an external content type for each set of data that you want to import, create a synchronization connection for each external content type, map the business system data to the user profile properties, and then perform the synchronization.