I am considering an itinerary that would involve a 5am (Lufthansa) departure from TLV for our flight back to the States. Will be with 2 kids. Seems miserable. Too early to bother getting a hotel the night before. Any bright ideas? Maybe get to the airport at 11pm, check in, go through security, and get a few hours sleep at the gate? Would that work with security at the airport, etc.?