db={"months":[{id:1,month:1,count:1},{id:1,month:2,count:2},{id:1,month:3,count:3},{id:2,month:1,count:1},{id:2,month:2,count:2},{id:2,month:3,count:3},{id:19,month:1,count:1},{id:19,month:2,count:2},{id:19,month:3,count:3}],"divisons":[{1:[1,2,4,5],2:[3,6,8,9],3:[7,10,19]}]}

db.divisons.aggregate([{$addFields:{data:{$filter:{input:{$objectToArray:"$$ROOT"},cond:{$isArray:"$$this.v"}}}}},{$unwind:"$data"},{$lookup:{from:"months",let:{ids:"$data.v"},pipeline:[{$match:{$expr:{$in:["$id","$$ids"]}}}],as:"months"}},{$unwind:"$months"},{$group:{_id:{divisionId:"$data.k",month:"$months.month"},count:{$sum:"$months.count"}}},{$project:{_id:0,divisionId:"$_id.divisionId",month:"$_id.month",count:"$count"}},{$sort:{divisionId:1,month:1}}])