You are mixing up a "protocol" with "data". There is no "LDAP data".
Apart from that, an LDAP directory can be seen as a classical example of persistent storage.
- LDAP directory entries have an average lifetime in the range of weeks, or even months.
- LDAP servers are optimized for an "occasional writes, many reads" usage pattern.
- Modern LDAP servers allow mechanisms for ensuring data consistency in the directory.