You can set the option:
to make lftp write the file transferred in ~/.lftp/transfer_log. Then you can simply send the file as attachment using mutt or uuencode. If you want the content of the file to be inserted in the mail sent by the cron job, just put
Code:
cat $HOME/.lftp/transfer_log
at the end of your script and it will be sent together with the standard output and the standard error of your script. Hope this helps.