diff --git a/.github/workflows/cla.yml b/.github/workflows/cla.yml
index 521e917e..ec3a953c 100644
--- a/.github/workflows/cla.yml
+++ b/.github/workflows/cla.yml
@@ -16,10 +16,27 @@ jobs:
     runs-on: ubuntu-latest
     steps:
       - uses: contributor-assistant/github-action@v2.6.1
+        # Run on close only if the PR was merged. This will lock the PR to preserve
+        # the CLA agreement. We don't want to lock PRs that have been closed without
+        # merging because the contributor may want to respond with additional comments.
+        # This action has a "lock-pullrequest-aftermerge" option that can be set to false,
+        # but that would unconditionally skip locking even in cases where the PR was merged.
         if: |
-          github.event_name == 'pull_request_target' ||
-          github.event.comment.body == 'recheck' ||
-          github.event.comment.body == 'I have read the CLA Document and I hereby sign the CLA'
+          (
+            github.event_name == 'pull_request_target' &&
+            (
+              github.event.action == 'opened' ||
+              github.event.action == 'synchronize' ||
+              (github.event.action == 'closed' && github.event.pull_request.merged == true)
+            )
+          ) ||
+          (
+            github.event_name == 'issue_comment' &&
+            (
+              github.event.comment.body == 'recheck' ||
+              github.event.comment.body == 'I have read the CLA Document and I hereby sign the CLA'
+            )
+          )
         env:
           GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
         with: