As Nummer says, read the whole email--it tells you why it was sent, and common reasons that it might not be a big deal. And if you got this one, you got two other emails, ten and twenty days ago, saying the same thing--so there's no reason this email should have sent you off in a panic.
Don't blame Let's Encrypt for your inability or unwillingness to read the whole message.
Well. I have read the email and it states one of my domains certificate has expired, plus a bunch of reasons why that statement might be wrong.
I know the renewal script runs every 24 hours, so my assumption is that something is not working correctly on that server. Of course,I could have assumed the email was wrong and ignored it, but that's not my way.
What baffle me is, whatever software issues the renewed certificate, seems to not tell the software that sends the emails about that event.
That was a good first thought and your actions were correct.
This is not what is happening. Please read the thread by @griffin above.
On a technical level, there is no distinction between a new certificate and a renewal - it's the same thing. Let's Encrypt attempts to guess certificates that are probably renewals based on the exact set of FQDNs. If this differs from your last certificate, the new certificate is not considered a renewal - because it looks completly different. Let's Encrypt doesn't know if the change of FQDNs was intentional from your side or not - hence the warning about a potentially expiring certificate.
It also links to an explanatory page on the Let's Encrypt documentation about what counts as a renewal and what does not. Please read that documentation too.
If you still require any assistance with your supposed issue, please provide the hostname or hostnames contained in the expiry e-mail, as I'm 99.999999999999 % certain this is not a bug in the expiry e-mailer, but just a misunderstanding.