You can use Redis as LRU cache - I am assuming that you are using Redis for in-memory operations only and PostgreSQL as your persistent datastore. The following URL sheds more light on using Redis as LRU cache:
http://redis.io/topics/lru-cache
You will need to write to both Redis and PostgreSQL (Redis will not write to PostgreSQL). It would be a good idea to briefly test and compare results against other options such as Memcached to figure out the best approach for your use case.
Also, the LRU cache implementation in Redis is different between v2.6 and v2.8 (not sure if the 2.8 changes were backported to v2.6 or not).
In case you are not familiar, you can persist data onto the disk vai Redis as well though you should be aware of memory limitations of using Redis as your sole data store (and impact on Redis for disk persistence).