MongoDB Aggregate to Fill an Array Where Not In Results - mongodb-query

Question

Simplifying the case, I have the following collections:
db.emails.find()
{ "_id" : ObjectId("5b59db643fd217eb78b1eb6d"), "title" : "abc" }
{ "_id" : ObjectId("5b59db643fd217eb78b1eb6e"), "title" : "def" }
and
db.users.find()
{ "_id" : ObjectId("5b59dbab3fd217eb78b1eb70"), "name" : "john", "forwarded" : [ObjectId("5b59db643fd217eb78b1eb6d")] }
{ "_id" : ObjectId("5b59dbac3fd217eb78b1eb71"), "name" : "mary", "forwarded" : [ObjectId("5b59db643fd217eb78b1eb6e")] }
where that forwarded column means all the emails that have already been forwarded to that given user.
I need to create something like this:
{ "_id" : ObjectId("5b59dbab3fd217eb78b1eb70"), "name" : "john", "forwarded" : [ {_id: ObjectId("5b59db643fd217eb78b1eb6d"), title: "abc"}], "not_forwarded" : [ {_id: ObjectId("5b59db643fd217eb78b1eb6e"), title: "abc"}] }
{ "_id" : ObjectId("5b59dbac3fd217eb78b1eb71"), "name" : "mary", "forwarded" : [ { _id: ObjectId("5b59db643fd217eb78b1eb6e"), title: "def" }], "not_forwarded" : [ { _id: ObjectId("5b59db643fd217eb78b1eb6d"), title: "def" }] }
By using aggregate.
So far, I have been able to create the "forwarded" part mappings, but I'm still trying to create the "not_forwarded" mapping.
I'm too much of a noob in the noSQL world to make this simple "outer join".
As I said, for the "forwarded" mapping, it was easy. I created something like this:
db.users.aggregate([
{ $lookup: { from: "emails", localField: "forwarded", foreignField: "_id", as: "forwarded"}},
{ $project: { "email_ids._id": 0, "email_ids.tile": 0}}
]);
Now, I'm trying to add the "not_forwarded" part, by adding some $match function, where (I guess) the clause would be a $nin aggregate, to fill inside the "not_forwarded" array, all the not yet sent items.
...and that's where I'm miserably failing.
Or in much simpler terms, I'm trying to come up with a query that will render all the emails that haven't yet been forwarded to the users in the DB.
Up to this day, I had it by making javascript loops, first in the emails' recordset, then nested inside, looping through all the users. Then creating a new recordset with all the pending emails to be sent.
This is ugly and non performatic. I would very much like to take full advantage of this aggregate mechanism to get these results.