diff --git a/lantern_hnsw/CMakeLists.txt b/lantern_hnsw/CMakeLists.txt
index 222b4870..f0b20830 100644
--- a/lantern_hnsw/CMakeLists.txt
+++ b/lantern_hnsw/CMakeLists.txt
@@ -268,6 +268,7 @@ set (_update_files
   sql/updates/0.3.4--0.4.0.sql
   sql/updates/0.4.0--0.4.1.sql
   sql/updates/0.4.1--0.5.0.sql
+  sql/updates/0.5.0--0.6.0.sql
 )
 
 # Generate version information for the binary
diff --git a/lantern_hnsw/sql/updates/0.5.0--0.6.0.sql b/lantern_hnsw/sql/updates/0.5.0--0.6.0.sql
new file mode 100644
index 00000000..370f442e
--- /dev/null
+++ b/lantern_hnsw/sql/updates/0.5.0--0.6.0.sql
@@ -0,0 +1,59 @@
+DO $$
+BEGIN
+    IF EXISTS (SELECT 1 FROM information_schema.tables WHERE table_schema = 'lantern' AND table_name = 'tasks') THEN
+        ALTER TABLE lantern.tasks ADD COLUMN pg_cron_jobid bigint DEFAULT NULL;
+    END IF;
+END $$;
+CREATE OR REPLACE FUNCTION _lantern_internal.async_task_finalizer_trigger() RETURNS TRIGGER AS $$
+DECLARE
+  res RECORD;
+BEGIN
+  -- if NEW.status is one of "starting", "running", "sending, "connecting", return
+  IF NEW.status IN ('starting', 'running', 'sending', 'connecting') THEN
+    RETURN NEW;
+  END IF;
+
+  IF NEW.status NOT IN ('succeeded', 'failed') THEN
+    RAISE WARNING 'Lantern Async tasks: Unexpected status %', NEW.status;
+  END IF;
+
+  -- Update pg_cron_jobid on lantern.tasks table before the job is unscheduled
+  -- This is necessary because under some circumstances jobs continue changing status even after they no longer
+  -- appear in cron.job. The easiest way to trigger this case is to schedule a multi-statement job
+  -- where the second statement causes a failure, e.g. async_task('select 1; select haha;')
+  UPDATE lantern.tasks t SET
+      pg_cron_jobid = c.jobid
+  FROM cron.job c
+  LEFT JOIN cron.job_run_details run
+  ON c.jobid = run.jobid
+  WHERE
+      t.pg_cron_job_name = c.jobname AND
+      c.jobid = NEW.jobid
+  -- using returning as a trick to run the unschedule function as a side effect
+  -- Note: have to unschedule by jobid because of pg_cron#320 https://github.com/citusdata/pg_cron/issues/320
+  -- Note2: unscheduling happens here since the update below may run multiple times for the same async task
+  --        and unscheduling same job multiple times is not allowed
+  --        At least experimentally so far, this update runs once per async task
+  RETURNING cron.unschedule(NEW.jobid) INTO res;
+
+  -- Get the job name from the jobid
+  -- Call the job finalizer if corresponding job exists BOTH in lantern async tasks AND
+  -- active cron jobs
+  UPDATE lantern.tasks t SET
+      (duration, status, error_message) = (run.end_time - t.started_at, NEW.status,
+      CASE WHEN NEW.status = 'failed' THEN return_message ELSE NULL END)
+  FROM cron.job_run_details run
+  WHERE
+      t.pg_cron_jobid = NEW.jobid
+      AND t.pg_cron_jobid = run.jobid;
+
+  RETURN NEW;
+
+EXCEPTION
+    WHEN OTHERS THEN
+        RAISE WARNING 'Lantern Async tasks: Unknown job failure in % % %', NEW, SQLERRM, SQLSTATE;
+        PERFORM cron.unschedule(NEW.jobid);
+        RETURN NEW;
+END
+$$ LANGUAGE plpgsql;
+