I flew out of TLV one January morning a few years ago...minimal lines. Arrived at the airport around 5am for my 8am departure and wound up spending a couple hours in the lounge. I was in business class on Austrian Airlines, though.

The guy and girl questioning me were polite and professional. I also had scary squiggly Arab stamps in my passport (did a tour of the middle east on that trip and flew home from Israel). They asked about them, but on the whole it was a pretty painless experience.