I did it (LDAP integration) for another things with asterisk, five years ago.
Here is short howto regarding SIP:
Make an crontab job which will
1. in cylce read all LDAP users and passwords
2. compare them with asterisk sip realtime database
3. if user details was updated (phone numbers, passwords) - do:
a) update sip realtime
b) update sip user (asterisk -rx "sip prune realtime USERNAME" && asterisk -rx "sip show peer USERNAME load")
4. By the end delete all non-existing in LDAP base, but existing in SIP realtime users and execute sip prune realtime USERNAME for each.
You can create this CLI script even with bash, but perl, php or ruby is much better.