Database

db={"plans":[{_id:ObjectId("6388024d0dfd27246fb47a5f"),"hight":10,"arquitec":"Aneesa Wade",},{_id:ObjectId("1188024d0dfd27246fb4711f"),"hight":50,"arquitec":"Smith Stone",},{_id:ObjectId("5a934e000102030405000002"),"hight":30,"arquitec":"Some One",}],"houses":[{"plansId":"6388024d0dfd27246fb47a5f","status":"incomplete",},{"plansId":"6388024d0dfd27246fb47a5f","status":"completed",},{"plansId":"5a934e000102030405000002","status":"completed",}]}

Query

db.houses.aggregate([{$match:{status:"completed"}},{$project:{_id:1,plansId:1,status:1,plans_id:{$toObjectId:"$plansId"}}},{$lookup:{from:"plans",localField:"plans_id",foreignField:"_id",as:"plan"}},{$project:{_id:1,plansId:1,status:1,plan:{$first:"$plan"}}},{$match:{"plan.arquitec":"Some One"}}])

Result