That's not a bad suggestion.
But IMHO even though some sort of email alert feature might be handy, I think it's a good management/survival strategy for any web manager to check their server logs (including Litespeed web server, but also your other logs, especially error logs) on a regular schedule. Like daily at least. There's a lot of things that can go wrong on a server through failures, misconfiguration and badness. Often times the problem may also happen outside of LSWS, so no alert might come anyhow.
So it might not be a good idea to rely on LSWS to do too much in terms of active error reporting.
There are also scripts you can get - depending on your platform - that can do stuff like monitor firewall, web server etc logs and do any alerting you need. A Google search will pull up tons of them, as will a browse around eg hotscripts. Some of these may be a better solution because they may be able to alert you to stuff failing or going awry outside of LSWS that you should also know about.