party-pooper

As stated, you want the "cats" so use the Cat model and do the "left outer join" that is actually inherent to $lookup, rather than asking for a "right outer join" from the opposing collection, since a "right outer join" is not possible with MongoDB at this time.

It's also far more practical as a "left join", because you want "cats" as your primary source of output. The only thing to consider when linking to "Party" is that each "Cat" is listed in an array, and therefore you get the whole document back. So all that needs to be done is in "post processing" after the $lookup, you simply "filter" the array content for the matching entry of the current cat.

Fortunately we get good features with $arrayElemAt and $indexOfArray, that allow us to do that exact extraction: