For Let’s Encrypt to automatically renew certificates on your Raspberry Pi, you probably want to install certbot. The installation instructions of certbot tell you to make use of the Debian Backports packages. Following the instructions to install backports packages into apt-get on raspbian (which is a Debian Jessie), you will probably run into the following error:
$ sudo apt-get update ... W: GPG error: http://ftp.debian.org jessie-backports InRelease: The following signatures couldn't be verified because the public key is not available: NO_PUBKEY 8B48AD6246925553 NO_PUBKEY 7638D0442B90D010