  Locally recoverable codes are error correcting codes with the additional
property that every symbol of any codeword can be recovered from a small set of
other symbols. This property is particularly desirable in cloud storage
applications. A locally recoverable code is said to have availability $t$ if
each position has $t$ disjoint recovery sets. Hermitian-lifted codes are
locally recoverable codes with high availability first described by Lopez,
Malmskog, Matthews, Pi\~nero-Gonzales, and Wootters. The codes are based on the
well-known Hermitian curve and incorporate the novel technique of lifting to
increase the rate of the code. Lopez et al. lower bounded the rate of the codes
defined over fields with characteristic 2. This paper generalizes their work to
show that the rate of Hermitian-lifted codes is bounded below by a positive
constant depending on $p$ when $q=p^l$ for any odd prime $p$.
