I'm not sure if I really understand what you're trying to achieve. Could you rephrase your question please?
When a person who is not in our group logs in lam.atlassian.com => error
Then the user will be redirected to the website: lamlumber.com.
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Ok so automation rules can not change the way users will login or be redirected on failed logins. Auatomation can basically act on things happening on Jira issues and then it perform some actions on them.
There is no way it can deal with user login events.
If you use a SSO provided you might be able to redirect users to another page after a failed login but I'm not 100% sure. It really depends on the SSO provider I guess.
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