You don't need a router for a LAN. You need a switch.
In order to ensure redundancy, you can have two switches. If each device has two network adapters, each device would be connected to each switch.
There are, then, different strategies.
You may keep the switches isolated from each other, and consider that you have two different networks.
Or you may connect both switches together and use LAG in order to pretend that each device has a single connection to the network, disregarding the fact that there are two physical connections.
I believe that the second solution is easier and more flexible, but I don't have too much skills in network stuff, so ask for advice on ServerFault. Also, switches which support LAG are rather expensive, so this may not be a solution for you.
Note that with two switches, you are still at risk that some of the device adapters stop working, and at the same time, the other switch stops working as well. If this is an issue, you may have, say, four interconnected switches, forming a switching loop—a technique often used to ensure redundancy. With four network adapters for every device, you reduce a lot the risk of losing connectivity to a device even in an event of a simultaneous breakage of a network adapter and a switch.