Delivery Method does not appear in the Catalog search criteria for LMS users. I have already checked: System Admin -> Configuration -> System Configuration -> Catalog -> the property 'catalogSearchFilters[Source]' is set to true.
Reproducing the Issue
Perform a catalog search as a user, try to filter by Delivery Method.
SInce none of items that show up in catalog search result have any delivery method, So the criteira doesn't show up an an option in catalog search criteria itself.
You could try providing a delivery method to any item then check back with the catalog search to see the criteria displayed.
Delivery Method Criteria , KBA , LOD-SF-LMS , SuccessFactors Learning , How To