Do you mean ATO online service via MyGov? MyGovID is something different and it's now called MyID.
If your issue is about doing your tax return via ATO online service, generally, the account would be indefinitely locked because of security reasons such as compromised TFN. You would need to call and get verified and then account is unlocked for 48 hours.
If you don't want to personally call, it may be worthwhile to do it via a tax agent. They do the phone call. [After you appoint them as your tax agent, whenever you make a date to do your tax return with them, then the day before you see them, the tax agent would make the phone call]