You can use one LRS with multiple sites however there are few downsides:
- Some features like LearnDash Groups integration works only with one WordPress site.
- Data is not 100% partitioned.
- Performance is affected if their is a lot of data, as all the statements are stored in one table.
Hence, it is best to have separate LRSes for separate sites.
However, if you decide to use one LRS, you can do this:
- Create separate LRS users/managers for each site.
- You can select "user" role, and "View Own Data" permission to ensure users don't see each others data.
- Generate Basic Authentication for each of them and use them for these sites.
- Create separate Triggers for each site, and select the user under Authority when adding/editing Triggers. Without this, completion data of one completion will be sent to all sites.