[{"_id":"ID_XXX","logs":[{"lead_id":123,"list_id":"list_44","order_id":"order_1"},{"lead_id":124,"list_id":"list_44","order_id":"order_2"}]},{"_id":"ID_YYY","logs":[{"lead_id":125,"list_id":"list_44","order_id":"order_2"},{"lead_id":126,"list_id":"list_44","order_id":"order_2"},{"lead_id":127,"list_id":"list_44","order_id":"order_3"},{"lead_id":128,"list_id":"list_66","order_id":"order_3"}]}]

db.collection.aggregate([{$addFields:{logs:{$filter:{input:{$reduce:{input:"$logs",initialValue:[],in:{$concatArrays:["$$value",{$objectToArray:"$$this"}]}}},cond:{$in:["$$this.k",["list_id","order_id"]]}}}}},{$unwind:"$logs"},{$group:{_id:{_id:"$_id",logs:"$logs"},counts:{$sum:1}}},{$group:{_id:"$_id._id",lists:{$push:{$cond:[{$eq:["$_id.logs.k","list_id"]},{k:"$_id.logs.v",v:"$counts"},"$$REMOVE"]}},orders:{$push:{$cond:[{$eq:["$_id.logs.k","order_id"]},{k:"$_id.logs.v",v:"$counts"},"$$REMOVE"]}}}},{$addFields:{lists:{$arrayToObject:"$lists"},orders:{$arrayToObject:"$orders"}}}])