How do I unlock my iCloud account when a different device is locked?

What do you mean "a different device is locked?"

If you have forgotten your Apple ID email, start here:

If you forgot your Apple Account primary email address or phone number - Apple Support

If you've forgotten the password, see here:

If you forgot your Apple Account password - Apple Support

If you mean something else, please explain.

If you have all the information about your Apple account, you can request a password reset by going to iCloud.com or iforgot. If you have a chance, you will get results.