db.coll1.find()
{ key: null }
db.coll2.find()
{ nested: { no_key: 42 } } 
{ nested: [ ] }
{ nested: [ [ ] ] }
{ nested: [ {no_key: 42} ] }

db.coll1.aggregate([{$lookup: {from:"coll2", localField:"key", foreignField:"nested.key", as:"matched"}}, {$project: {_id:0, "matched._id":0}}])
produces
{ "key" : null, "matched" : [ { "nested" : { "no_key" : 42 } }, { "nested" : [ { "no_key" : 42 } ] } ] }
That is, docs where the "nested.key" path in foreign traverses through an empty array aren't matched to null.

db.coll2.aggregate([{$lookup: {from:"coll1", localField:"nested.key", foreignField:"key", as:"matched"}}, {$project: {_id:0, "matched._id":0}}])
produces
{ "nested" : { "no_key" : 42 }, "matched" : [ { "key" : null } ] }
{ "nested" : [ ], "matched" : [ { "key" : null } ] }
{ "nested" : [ [ ] ], "matched" : [ { "key" : null } ] }
{ "nested" : [ { "no_key" : 42 } ], "matched" : [ { "key" : null } ] }