Please fill out the fields below so we can help you better. Note: you must provide your domain name to get help. Domain names for issued certificates are all made public in Certificate Transparency logs (e.g. crt.sh | example.com), so withholding your domain name here does not increase secrecy, but only makes it harder for us to provide help.
I'm the person in charge of PunchLab. Recently, a server developer left the company and received two certificate expiration notice emails from the punchylab.dev@gmail.com account. However, it is difficult to respond because we have not received a specific handover for the account.
The quick answer is that communication with Let's Encrypt all happens over an API from an automated system. So there's some software running on your servers, which is handling renewing and installing those renewed certificates wherever they need to go.
If that system isn't working, you would need to look at its logs to find the error message to figure out what exactly is the problem, to fix it and allow it to once again automatically renew and install your certificates.
There's no "authority" associated with the email address that's on an ACME account. You can change it if you want to, using the protocol. For instance, the popular client certbot has a certbot update_account command. But that would just change the location for possible future notifications. (And in general, it doesn't really have much of a difference from just creating a new account with the new email address, unless you have some rate limit exceptions or the like tied to your existing account.) And as stated above, Let's Encrypt is moving away from doing any account-specific notifications for privacy reasons, and recommends just subscribing to their newsletters if you want to stay up-to-date on what they're doing.