Yeah, we can do stuff like this, but a fair chunk of it will have to be done by hand (by you for free, or us for money!).
Basically you'd just get 2 servers and we'd set services up on them that are almost identical, get the replication going, and if/when the first server died, we'd move the IPs for your sites to the 'backup' server. And if you have content (on disk) that gets updated frequently, we'd maybe NFS mount that data and make local copies.
Which is to say there'd be no "real" load balancer involved, so it wouldn't be hot-failover, but it'd be better than nothing and easy to get the "backup" server going.
But it's not something that's manageable via the Panel. So you'd need to pay us to set up the NFS mounts, replication, etc or do it yourself.
We've had people ask us about using a real load-balancer but we've never had someone bite, mostly because load-balancers tend to be on the expensive and tricky side.
But yeah, if you're interested, write in and get a conversation going about it.