Have you checked to make sure the 3rd and 4th lines subscribe to the Caller ID service?
Does it always fail on the 3rd or 4th lines or is it intermittent?
Here are a couple of things you can test or check.
For this test, you'll need a test set you can connect to the 3rd or 4th line to monitor the line while a call is ringing in. You can test caller ID by calling the 3rd or 4th lines directly and listening for tones between the 1st and 2nd ring; this is the caller ID data. If there is the burst of tones between the 1st and 2nd rings, it could be the telco isn't sending the correct caller ID data for that line. Also, the 7965 may be picking up the call before the caller ID tones are sent. If he/she picks the call up on the 1st ring, the caller ID may not be sent and Unknown would be displayed. I don't know if the router where the FXO ports terminate automatically waits for the caller ID tones before presenting the call to the 7965.
I'm sure there are debugs you can run on the router to see what caller ID is being sent by the telco but I'm not familiar with those debugs.
Bill