Database

db={"users":[{"_id":{"$oid":"603d4c44505a51001c9b936f"},"email":"mister.paper@papers.org","name":"Mister Paper","profile":{"products":[{"_id":{"$oid":"603d4d101c24a9001cf79db1"},"product":{"$oid":"5dd5a66e8ddbd07fa251b88e"},"profile":{"$oid":"5e94da0f4d499253049ec534"}},{"_id":{"$oid":"603fe3ebca063ea357ca0666"},"product":{"$oid":"5e8b40bc91dd0e12e0219578"},"profile":{"$oid":"5e8b40bc91dd0e12e0219579"}},{"_id":{"$oid":"603fe3ebca063ea357ca0667"},"product":{"$oid":"5dd5a66e8ddbd07fa251b88e"},"profile":{"$oid":"5e94da0f4d499253049ec538"}}],},"username":"mister.paper@papers.org"}],"products":[{"_id":{"$oid":"5dd5a66e8ddbd07fa251b88e"},"name":"Product One","internals":[{"default":false,"_id":{"$oid":"5e94da0f4d499253049ec532"},"name":"Type A"},{"_id":{"$oid":"5e94da0f4d499253049ec534"},"name":"Type B"},{"_id":{"$oid":"5e94da0f4d499253049ec536"},"name":"Type C"},{"_id":{"$oid":"5e94da0f4d499253049ec538"},"name":"Type D"},{"_id":{"$oid":"5f05d9a2bfc8fa1361d8beea"},"name":"Type E"},{"_id":{"$oid":"5f05d9a2bfc8fa1361d8beec"},"name":"Type F"}]},{"_id":{"$oid":"5e8b40bc91dd0e12e0219578"},"name":"Product Two","internals":[{"_id":{"$oid":"5e8b40bc91dd0e12e0219579"},"name":"Default Type"}],}]}

Query

db.users.aggregate([{$unwind:"$profile"},{$unwind:"$profile.products"},{$unwind:"$profile.products.profile"},{"$lookup":{from:"products",localField:"profile.products.product",foreignField:"_id",as:"products"}},{$unwind:"$products"},{"$addFields":{"internal":{$filter:{input:"$products.internals",as:"i",cond:{"$eq":["$$i._id","$profile.products.profile"]}}},}},{"$project":{_id:1,name:1,"profile.products":1,products:{name:1,_id:1},internal:{_id:1,name:1},}}])

Result