How does an LRU cache fit into the CAP theorem?

I was pondering this question today. An LRU cache in the context of a database in a web app helps ensure Availability with fast data lookups that do not rely on continually accessing the database.

However, how does an LRU cache in practice stay fresh? As I understand it, one cannot garuntee Consistency along with Availibility. How is a frequently used item, which therefore does not expire from the LRU cache, handle modification? Is this an example where in a system that needs C over A, an LRU cache is not a good choice?