Assuming that Citadel will accept standard PEM-encoded key/cert/chain, configure it to look in /etc/letsencrypt/live/{your hostname}/privkey.pem, cert.pem, and chain.pem for those things. When you renew the cert, those file pathnames will remain the same, so no reconfiguration will be necessary.
http://www.citadel.org/doku.php/faq:systemadmin:how_to_install_a_certificate_signed_by_a_recognized_certificate_authority appears to have some information, but makes it look like Citadel expects those files to only be in a certain defined location–idiotic software design if so, but you should be able to create symlinks to the files in /etc/letsencrypt/live/.