Shared LUN for SQL Server Backup files
Technically there should be no issue with backups being written to a shared LUN.  

As you are using 2012 you do have the option of sending backups to a network share as well which could reduce the complexity of the cluster if you have a fileserver that you can use just to reduce the overhead in a DR situation (as in not having to add the LUN to the cluster etc etc).

Looking at a couple of guides and articles around the place backup drives shared to the nodes is a common thing.

https://mssqltrek.com/2012/06/28/how-to-add-a-new-diskdrive-to-sql-server-failover-cluster/

Fairly verbose example of said process but confirms the validity of backups on shared storage in a cluster.