Hi adfser,
According to the error message "http://fs.corp.contoso.com/adfs/services/trust, HTTP Error 503. The service is unavailable", it can be caused by a Relying Party trust. I understand you have updated the Relying Party trust. I'd like to confirm if you manually new a Relying Party Trust or create a claim rule for a Relying Party Trust. Please check the settings referring to the link below: http://technet.microsoft.com/en-us/library/dd807108.aspx
Also, based on the error message "https://fs.corp.lisystec.com/adfs/ls/federationserverservice.asmx【Error】An error occurred", it turns out that the federation server is not operational. Internet Information Services (IIS) may be configured incorrectly on the federation server. Please check the certificate, then restart the IIS service with “iisreset” command.
Finally, please run Update-MSOLFederatedDomain -DomainName domain.com after changing AD FS settings.
Thanks,
Edward Qu
