Actually, I have found the same issue and I am able to use the new certificate the following way:
1. Open the Lets Encrypt entry in the menu and select your certificate.
2. from the options, select "Renew certificate". It will tell you that no renewal is needed as the certificate is not yet due to renewal.
3. You will get the "Apply changes" dialog. Once you click apply, the new certificate will be used.
My question would be:
Why is the Lets Encrypt plugin not able to handle that configuration update on its own once the certificate got renewed?
Anybody able to answer that?