From the logwatch README:
How do I use it?
Well, it should pretty much work on its own, sending you an
email every night. For more configuration options, run
'logwatch --help' or edit /usr/share/logwatch/default.conf/logwatch.conf
or /etc/logwatch/logwatch.conf.
See the file HOWTO-Customize-LogWatch for more information.
You can also use it from the command line (as documented in the
man page).
I could run it successfully from the command line also and view the output on screen, but couldn't get it to work using cron in cPanel. What I DID have to do was customize the default conf file. This file is very well commented, and I only made 3 changes: email address, range (Yesterday) and detail level.
So I think trying to run it from cron might be redundant. I had it working on my old VPS, and when I checked the crontab there, found I didn't have an entry for it. In that case I did a yum install, though. On my new server it was already installed.
Logwatch seems to have it's own cron function. But now that I've modified that default conf file - I ran it from the CLI once, just to check that it was working - it sends me an email every night, running about 3:00 am (server time).
If you're still having trouble you might want to go to the source and check the logwatch.org web site. Let us know how this worked out for you.