An answer based off Jean-Luc Boss's and wiak's, but a bit more explicit:
To connect to a server, lftp uses an ssh command, by default ssh -a -x. It doesn't have an explicit option for changing the keyfile to use, but as you note, ssh does, so we just need to set lftp to connect using ssh -a -x -i before it connects.
You can do this in a few ways:
If you're using lftp's interactive command line, run the following command before you connect:
set sftp:connect-program "ssh -a -x -i "
If you're specifying a bunch of commands to lftp using -c, just add that set command to the start of your command sequence:
lftp -c 'set sftp:connect-program "ssh -a -x -i "; connect sftp://user@example.com; mirror -eR files; ...'
If you always going to want to use the same key, just add that set ... line from the first bullet to your ~/.lftprc file (or one of the other configuration file options listed in man lftp).
