We currently do not offer Redis or Memcached on our shared hosting.
While Memcached is available to offer under shared hosting via LSCMD (LiteSpeed Memcached), LSCMD is not something we're currently offering or plan to offer.
Redis is also not available at this moment, due to how Redis works. Redis in itself doesn't have any good multi-user functionality. The latest version of Redis added basic authentication capabilities, but nowhere secure enough to be offered in a shared hosting environment.
We're looking into offering Redis in the future, this, however, requires special development to utilize some of the security features we have available to us (Mainly utilizing CageFS from CloudLinux). We do currently not have any ETA when Redis will be available.