Or a cronjob.
You can also set a management server to delete old logs when lv_log has under X gigabytes of free space.
Strictly, it should be possible to grant a specific user RWX access to everything under a directory using extended filesystem ACLs. New files would be created with the default permissions from the umask, though, so the user wouldn't be able to remove most logs, so a cronjob or similar would still be needed to apply the ACL. May as well have the cronjob handle the cleanup directly.