I use a MacBook Pro and Lightroom 5, with an external hard disk to save the photo files.
To back up the machine I use Time Machine.
To back up the external hd to another hd what software to use?
I question your premise: that to create another backup, that you want to back up the backup.
Let me explain, in a longwinded fashion:
I've been working with computers for more than fifty years, almost as long as I've been making photographs. I retired about 15 years ago, and, when non-profits find out about my computer R&D experience, and, more to the point, my briefer time as a CIO, they want me to consult. I always agree.
I love to consult before the disaster. It's not so much fun to be called in after the disaster.
Many of the disasters revolve around backup. Or rather, the backup that wasn't. Or sometimes, the backup that backed up the wrong files. More than occasionally, the backup that stopped backing up, but never told me. And, most sadly, the restore that didn't.
When called in after the fact, I do my best to facilitate the (too often partial) recovery. When called in early, I stress that backups are only as dependable as the monitoring systems. IMHO, set and forget backups are great for generating a feeling of confidence, but taking confidence to your board after a failed recovery is cold comfort.
You should monitor your backup system to make sure it's doing what you think it is. The only sure way to do that is with trial restores. With cloning systems, that means wiping out a version of the backed-up system. Most people are scared to do that, and don't. With systems like Time Machine, that store data in a proprietary chunked format, it means file-level trial restores. Most people won't do that either. If you do it religiously, forget what I'm about to say.
My advice: rather than back up the files that Time Machine produces, do a parallel backup from your originals to another target using a file-based backup program like GoodSync. Then you'll be able to test the backup (and you should) by opening the backed up files. Thus you'll have two independent backup paths: the Time Machine one, which is great for recovering from too-quick finger motions, and the file-based one, which is verifiable.
Here's a fuller discussion.Jim