Firts you need to enable mod_openssl
/usr/sbin/lighttpd-enable-mod ssl
Then edit /etc/lighttpd/conf-enabled/10-ssl.conf :
vi /etc/lighttpd/conf-enabled/10-ssl.conf
Adjust to:
ssl.pemfile := "/etc/letsencrypt/live/example.com/fullchain.pem"
ssl.privkey := "/etc/letsencrypt/live/example.com/privkey.pem"
and restart:
sudo service lighttpd restart
Note that the pemfile must be fullchain.pem and NOT just cert.pem Otherwise while in browser all works you'll get and errors on connection:
wget: ERROR: cannot verify certificate, issued by 'CN=R3,O=Let's Encrypt,C=US' Unable to locally verify the issuer's authority
curl: SSL certificate problem: unable to get local issuer certificate curl: (60) SSL certificate problem: unable to get local issuer certificate