diff --git a/certbot/interfaces.py b/certbot/interfaces.py
index 6233e3592..a5fb426e6 100644
--- a/certbot/interfaces.py
+++ b/certbot/interfaces.py
@@ -604,10 +604,10 @@ class IReporter(zope.interface.Interface):
 # When "certbot renew" is run, Certbot will iterate over each lineage and check
 # if the selected installer for that lineage is a subclass of each updater
 # class. If it is and the update of that type is configured to be run for that
-# lineage, the relevant update function will be called for each domain in the
-# lineage. These functions are never called for other subcommands, so if an
-# installer wants to perform an update during the run or install subcommand, it
-# should do so when :func:`IInstaller.deploy_cert` is called.
+# lineage, the relevant update function will be called for it. These functions
+# are never called for other subcommands, so if an installer wants to perform
+# an update during the run or install subcommand, it should do so when
+# :func:`IInstaller.deploy_cert` is called.
 
 @six.add_metaclass(abc.ABCMeta)
 class GenericUpdater(object):
@@ -623,7 +623,7 @@ class GenericUpdater(object):
     """
 
     @abc.abstractmethod
-    def generic_updates(self, domain, *args, **kwargs):
+    def generic_updates(self, lineage, *args, **kwargs):
         """Perform any update types defined by the installer.
 
         If an installer is a subclass of the class containing this method, this
@@ -631,9 +631,10 @@ class GenericUpdater(object):
         update defined by the installer should be run conditionally, the
         installer needs to handle checking the conditions itself.
 
-        This method is called once for each domain.
+        This method is called once for each lineage.
 
-        :param str domain: domain to handle the updates for
+        :param lineage: Certificate lineage object
+        :type lineage: storage.RenewableCert
 
         """
 
@@ -661,8 +662,7 @@ class RenewDeployer(object):
 
         This method is called once for each lineage renewed
 
-        :param lineage: Certificate lineage object that is set if certificate
-            was renewed on this run.
+        :param lineage: Certificate lineage object
         :type lineage: storage.RenewableCert
 
         """
diff --git a/certbot/tests/renewupdater_test.py b/certbot/tests/renewupdater_test.py
index 9d0f8d515..ade8db390 100644
--- a/certbot/tests/renewupdater_test.py
+++ b/certbot/tests/renewupdater_test.py
@@ -19,7 +19,7 @@ class RenewUpdaterTest(unittest.TestCase):
                 # pylint: disable=unused-argument
                 self.restart = mock.MagicMock()
                 self.callcounter = mock.MagicMock()
-            def generic_updates(self, domain, *args, **kwargs):
+            def generic_updates(self, lineage, *args, **kwargs):
                 self.callcounter(*args, **kwargs)
 
         class MockInstallerRenewDeployer(interfaces.RenewDeployer):
@@ -46,9 +46,7 @@ class RenewUpdaterTest(unittest.TestCase):
     def test_server_updates(self, _, mock_select, mock_getsave):
         config = self.get_config({"disable_renew_updates": False})
 
-        lineage = mock.MagicMock()
-        lineage.names.return_value = ['firstdomain', 'seconddomain']
-        mock_getsave.return_value = lineage
+        mock_getsave.return_value = mock.MagicMock()
         mock_generic_updater = self.generic_updater
 
         # Generic Updater
@@ -59,14 +57,13 @@ class RenewUpdaterTest(unittest.TestCase):
 
         mock_generic_updater.restart.reset_mock()
         mock_generic_updater.callcounter.reset_mock()
-        updater.run_generic_updaters(config, None, lineage)
-        self.assertEqual(mock_generic_updater.callcounter.call_count, 2)
+        updater.run_generic_updaters(config, None, mock.MagicMock())
+        self.assertEqual(mock_generic_updater.callcounter.call_count, 1)
         self.assertFalse(mock_generic_updater.restart.called)
 
     def test_renew_deployer(self):
         config = self.get_config({"disable_renew_updates": False})
         lineage = mock.MagicMock()
-        lineage.names.return_value = ['firstdomain', 'seconddomain']
         mock_deployer = self.renew_deployer
         updater.run_renewal_deployer(lineage, mock_deployer, config)
         self.assertTrue(mock_deployer.callcounter.called_with(lineage))
diff --git a/certbot/updater.py b/certbot/updater.py
index f822c55ee..1216f38a6 100644
--- a/certbot/updater.py
+++ b/certbot/updater.py
@@ -61,7 +61,6 @@ def _run_updaters(lineage, installer, config):
     :returns: `None`
     :rtype: None
     """
-    for domain in lineage.names():
-        if not config.disable_renew_updates:
-            if isinstance(installer, interfaces.GenericUpdater):
-                installer.generic_updates(domain)
+    if not config.disable_renew_updates:
+        if isinstance(installer, interfaces.GenericUpdater):
+            installer.generic_updates(lineage)