To get a list of all groups to which a user belongs (excluding Livelink Project membership groups), there is a built-in query that can be accessed from the "Enterprise" menu at the top of any Livelink page. Select Enterprise --> Users and Groups, locate the user in question, then click the "Groups" link in the "Action" column next to that user's name. Only the Livelink Admin has access to this built-in function. Regular Livelink users only see a "View" option in the Actions column.
If you wish to set up a LiveReport to produce a list of all groups to which a user belongs, and are using an Oracle database with Livelink, an exhaustive answer to this question can be found at the following location in the Open Text Knowledge Centre:
https://knowledge.opentext.com/knowledge/llisapi.dll?func=ll&objId=2627549&objAction=view&show=2