I am looking for some ideas on how I can accomplish this:
Right now, for our website that is hosted on our own servers, we have a load balancer that redirects the user to another server if our web servers are down. This works great if our load-balancer never fails and if we never lose connectivity.
What would be ideal is to have web traffic routed to a third-party host in the instance that we lose connectivity or the load-balancer is unavailable. How could I accomplish this?
The brief answer is that you will need a load balancer outside of your data center instead of inside your datacenter. Setup redundant load balancers at a good colo center. Then you can have fail over to another location in the case of power outage, network connectivity, server outage, etc. Usually a colo center is much better equiped to handle the network connectivity and power issues than most self-hosted sites.
Of course you need to determine if you need that type of SLA.
We use zoneedit.com and their failover server. If our main site goes done Zoneedit chagnes the DNS to the backup server- Works great and is very affordable.
You should look at global load balancing (GSLB).
Basically, you have a DNS server that resolved your web site IP address. The DNS server is monitoring your active site and your backup site. If the active site goes down, the DNS server resolves your website to the IP address of the secondary site. This way, you can have a whole site go down, and your users will be redirected via new DNS resolution to your backup site.
F5 has a good product (but $$$) that does this stuff.
