There is a transit are, but I have never seen anyone use it.
I did. And since then I would second what danielbk recommends: going through immigration and reentering.
Not because the staff is rude. On the contrary on my many trips to TLV I never met one unhelpful, rude or impolite security worker or ben-gurion-employee. But they are really thorough...(for obvious reasons). And the procedure will take time.
Transit is uncommon and needs to be preannounced.
You take a right at the rotunde and go down one flight of stairs. There you will find yourself infront of a locked door leading to the transit security check area. You will have to call security via wall mounted phone.
In my case it took them 12min. And it gave me a chance to have a close look. Judged by the spider webs and the dust, this transit security area is seldomly used.
Then they arrived. 7 young TLV-security people, lead by a charming senior agent, approx 30 years old.
And they gave me a good treatment which took some 40mins. Don't get me wrong, not complaining, they were polite, friendly and smiling. But they checked everything. xrazed my handluggage several times, took everzthing out, scanned it again, swiped it, checked my purse, my shoes, my belt, patted me down 2 times. Continuosly asked questions what I am doing and why I am transiting. And even interviewed the folks waiting for me in the transit area.
Because transit is very uncommon.
Regarding online check in. I had a printed bp with me, that did not matter. Did not safe me any time. When phoning them, they asked from which flight I was coming and to which I was connecting. A nice lady from LH came 20mins into the procedure to the transit security checknd and after they were finished with me, she give me a "proper" bp and hustled me to the gate.