This is actually fairly common to have issues with the LAB_PROJECT.
With the enterprise/QC license The ''Lab Management'' tab is hidden and normally you cannot see the Lab_Project.
Normally, a new LAB_PROJECT gets created with every install and the installer will attempt to upgrade an existing one if it finds the LAB_PROJECT (named something like ''default_lab_project_db'').
Now, since you are using the Enterprise license, you are not using the Lab_Project anyway (it is part of server-side test automation feature exposed with the ALM license), you can use the new/blank one, or try to manually upgrade the old one if needed.
So, the first thing to try would be to expose the LAB_PROJECT in your project list. See this post on how to add the site parameter to do that:
Then, it can be treated like a ''regular'' project and you can perform a VERIFY/REPAIR/UPGRADE as usual on it.
NOTE: In this state you now CAN ''restore'' a LAB_PROJECT like you do ''regular'' projects.
IF you for some reason don't have a LAB_PROJECT (look in the qcsiteadmin_db/PROJECTS table to see if it is there), you can re-run the configuration wizard (not re-install) and it will create a new blank one and put in the list -- don't forget to tell it to use an EXISTING qcsiteadmin_db and point to your already-upgraded one.
IF you can find an EXISTING LAB_PROJECT (database like ''default_lab_project_db'' + corresponding repository), AND it is in the PROJECTS table, you COULD just fix the DB entry for the project so it points to it properly (correct names, paths, URL's etc.), OR you could RESTORE it like a''regular'' project (assuming you set the site parameter).
If using ORACLE, make sure this ''schema-user'' has the SAME password as your ''regular'' project schemas have and then copy the encrypted password string to this row in the table.
So, all QC wants here is a WORKING/UPGRADED Lab_Project.
When restoring or creating projects, it needs to communicate with this project so it knows about all projects in case it would be used in Server-side test automation -- Even though you don't have the feature.