Terms Lookup + sort

Not through the terms lookup functionality. You can think of that as merely grabbing the list of terms to filter from a document, rather than from the query body supplied as part of the request.

But you can add a sort element to your query which does the sorting:

GET /users/user/_search
{
      "query":{
         "terms":{
            "id":{
               "index":"newsfeed",
               "type":"feed",
               "id":"1",
               "path":"likers.id"
            }
         }
      },
      "sort" : [
          { "likers.id" : {"order" : "asc"}},
          "_score"
      ],
}

Note that unless that first document is using Nested Documents (you can also read more here) your relationships in the document may not be preserved like you think they are.