If you’re using an external address book in Thunderbird, all contact actions are still done on the default build-in address book, and there’s no option to mark another address book as being the default one.
The only solution is to go into the advanced config editor and change ldap_2.servers.pab.dirType to -1, default value is 2.
To do this open the address book (CTRL-SHIFT-B) and go to Edit -> Preferences -> Advanced -> Config Editor, search for ldap_2.servers.pab.dirType and change the value to -1. Close all the screens, quit thunderbird and restart it.