[{"art":[{"art":"123","public":false},{"art":"321","public":true}],"artFoundByLookup":[{"_id":"123","name":"Art 1","artist":"Artist 1"},{"_id":"321","name":"Art 2","artist":"Artist 2"}]}]

db.collection.aggregate([{$addFields:{Entities:{$map:{input:"$art",as:"e",in:{$mergeObjects:["$$e",{$arrayElemAt:[{$filter:{input:"$artFoundByLookup",as:"j",cond:{$eq:["$$e.art","$$j._id"]}}},0]}]}}}}},{$project:{art:"$Entities"}}])