Database

db={"collection":[{"_id":ObjectId("5ce7454f77af2d1143f84c38"),"menu_name":"mainmenu1","sub_menus":["submenu1","submenu2"]}],"project":[{"project_name":"p1","sub_menus":"submenu1",},{"project_name":"p2","sub_menus":"submenu2",}]}

Query

db.collection.aggregate([{"$lookup":{"from":"project","let":{"sub_menus":"$sub_menus"},pipeline:[{$match:{$expr:{$in:["$sub_menus","$$sub_menus"]}}},{$project:{projectData:[{project_name:"$project_name"}],sub_menu_name:"$sub_menus"}}],"as":"sub_menus"}}])

Result