I have a use case where I need an email sent to the survey admin, but only in the case where certain conditions are true in the survey. Is there a way to send admin email only certain condition is true (like a question that asks "Do you want us to follow up with you by phone?" And if answer is Yes, then the admin notification email is sent? And if No, then admin isn't sent?

Yes, you can use Expression Manage/Script in the notification email settings.

Excellent, I will test this out. I assume then if the template message body is empty due to the condition returning an empty value, the admin notification won't be sent, or do I also need to have the condition in the subject line?

No : use expressio directly inside notification email : www.limesurvey.org/manual/Notifications_..._notifications_email

For example {if(Q01 > 1, 'userOK@example.org',if(Q01 < -1, 'userOK@example.org',''))}

My advice : use an equation quetsion directly , and just put {MyEquationEmail} in the setting.